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Journal articles on the topic 'Graphe quasi-Bipartite'

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Published: 7 July 2024

Last updated: 7 July 2024

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1

Ma, Junye, Qingguo Li, and Hui Li. "Some properties about the zero-divisor graphs of quasi-ordered sets." Journal of Algebra and Its Applications 19, no. 04 (June 12, 2019): 2050074. http://dx.doi.org/10.1142/s0219498820500747.

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In this paper, we study some graph-theoretic properties about the zero-divisor graph [Formula: see text] of a finite quasi-ordered set [Formula: see text] with a least element 0 and its line graph [Formula: see text]. First, we offer a method to find all the minimal prime ideals of a quasi-ordered set. Especially, this method is applicable for a partially ordered set. Then, we completely characterize the diameter and girth of [Formula: see text] by the minimal prime ideals of [Formula: see text]. Besides, we perfectly classify all finite quasi-ordered sets whose zero-divisor graphs are complete graphs, star graphs, complete bipartite graphs, complete [Formula: see text]-partite graphs. We also investigate the planarity of [Formula: see text]. Finally, we obtain the characterization for the line graph [Formula: see text] in terms of its diameter, girth and planarity.

2

Kumar, P. Ramana Vijaya, and Dr Bhuvana Vijaya. "Applications of Hamiltonian Cycle from Quasi Spanning Tree of Faces based Bipartite Graph." Journal of Advanced Research in Dynamical and Control Systems 11, no. 12-SPECIAL ISSUE (December 31, 2019): 505–12. http://dx.doi.org/10.5373/jardcs/v11sp12/20193245.

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3

Ansari-Toroghy, Habibollah, Shokoufeh Habibi, and Masoomeh Hezarjaribi. "On the graph of modules over commutative rings II." Filomat 32, no. 10 (2018): 3657–65. http://dx.doi.org/10.2298/fil1810657a.

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Let M be a module over a commutative ring R. In this paper, we continue our study about the quasi-Zariski topology-graph G(?*T) which was introduced in (On the graph of modules over commutative rings, Rocky Mountain J. Math. 46(3) (2016), 1-19). For a non-empty subset T of Spec(M), we obtain useful characterizations for those modules M for which G(?*T) is a bipartite graph. Also, we prove that if G(?*T) is a tree, then G(?*T) is a star graph. Moreover, we study coloring of quasi-Zariski topology-graphs and investigate the interplay between ?(G(?+T)) and ?(G(?+T)).

4

Naji Hameed, Zainab, and Hiyam Hassan Kadhem. "On Degree Topology and Set-T_0 space." Wasit Journal of Computer and Mathematics Science 1, no. 4 (December 31, 2022): 213–19. http://dx.doi.org/10.31185/wjcm.91.

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This work is aimed to introduce a new topology on a graph, namely the degree topology. This topology is defined by the degree of the vertices of the graphs. We find the degree topology for certain types of graphs and determine their types. The degree topology for the complete graph is an indiscrete topology. While The degree topology is generated by a complete bipartite graph with is a quasi-discrete topology. In addition, a new property is initiated namely set- space and discussed the link between it and space. We verify that every degree topology is a set- space.

5

Gröpl, Clemens, Stefan Hougardy, Till Nierhoff, and Hans Jürgen Prömel. "Steiner trees in uniformly quasi-bipartite graphs." Information Processing Letters 83, no. 4 (August 2002): 195–200. http://dx.doi.org/10.1016/s0020-0190(01)00335-0.

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6

Bagheri Gh., Behrooz, Tomas Feder, Herbert Fleischner, and Carlos Subi. "On Finding Hamiltonian Cycles in Barnette Graphs." Fundamenta Informaticae 188, no. 1 (December 27, 2022): 1–14. http://dx.doi.org/10.3233/fi-222139.

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In this paper we deal with hamiltonicity in planar cubic graphs G having a facial 2–factor 𝒬 via (quasi) spanning trees of faces in G/𝒬 and study the algorithmic complexity of finding such (quasi) spanning trees of faces. Moreover, we show that if Barnette’s Conjecture is false, then hamiltonicity in 3–connected planar cubic bipartite graphs is an NP-complete problem.

7

Liu, Meng, and Yusheng Li. "Ramsey numbers and bipartite Ramsey numbers via quasi-random graphs." Discrete Mathematics 344, no. 1 (January 2021): 112162. http://dx.doi.org/10.1016/j.disc.2020.112162.

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8

Ben-Ari, Iddo, Hugo Panzo, Philip Speegle, and R. Oliver VandenBerg. "Quasi-Stationary Distributions for the Voter Model on Complete Bipartite Graphs." Latin American Journal of Probability and Mathematical Statistics 18, no. 1 (2021): 421. http://dx.doi.org/10.30757/alea.v18-19.

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9

Rowlinson, Peter. "More on graphs with just three distinct eigenvalues." Applicable Analysis and Discrete Mathematics 11, no. 1 (2017): 74–80. http://dx.doi.org/10.2298/aadm161111033r.

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Let G be a connected non-regular non-bipartite graph whose adjacency matrix has spectrum p,?(k),?(l), where k,l ? N and p > ? > ?. We show that if ? is non-main then ?(G) ? 1 + ? - ??, with equality if and only if G is of one of three types, derived from a strongly regular graph, a symmetric design or a quasi-symmetric design (with appropriate parameters in each case).

10

Yu, Guidong, Gaixiang Cai, Miaolin Ye, and Jinde Cao. "Energy Conditions for Hamiltonicity of Graphs." Discrete Dynamics in Nature and Society 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/305164.

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LetGbe an undirected simple graph of ordern. LetA(G)be the adjacency matrix ofG, and letμ1(G)≤μ2(G)≤⋯≤μn(G)be its eigenvalues. The energy ofGis defined asℰ(G)=∑i=1n‍|μi(G)|. Denote byGBPTa bipartite graph. In this paper, we establish the sufficient conditions forGhaving a Hamiltonian path or cycle or to be Hamilton-connected in terms of the energy of the complement ofG, and give the sufficient condition forGBPThaving a Hamiltonian cycle in terms of the energy of the quasi-complement ofGBPT.

11

Albuquerque, C. D., R. Palazzo Jr., and E. B. Silva. "New classes of TQC associated with self-dual, quasi self-dual and denser tessellations." Quantum Information and Computation 10, no. 11&12 (November 2010): 956–70. http://dx.doi.org/10.26421/qic10.11-12-6.

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In this paper we present six classes of topological quantum codes (TQC) on compact surfaces with genus $g\ge 2$. These codes are derived from self-dual, quasi self-dual and denser tessellations associated with embeddings of self-dual complete graphs and complete bipartite graphs on the corresponding compact surfaces. The majority of the new classes has the self-dual tessellations as their algebraic and geometric supporting mathematical structures. Every code achieves minimum distance 3 and its encoding rate is such that $\frac{k}{n} \rightarrow 1$ as $n \rightarrow \infty$, except for the one case where $\frac{k}{n} \rightarrow \frac{1}{3}$ as $n \rightarrow \infty$.

12

Lai, Xinsheng, Yuren Zhou, Xiaoyun Xia, and Qingfu Zhang. "Performance Analysis of Evolutionary Algorithms for Steiner Tree Problems." Evolutionary Computation 25, no. 4 (December 2017): 707–23. http://dx.doi.org/10.1162/evco_a_00200.

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The Steiner tree problem (STP) aims to determine some Steiner nodes such that the minimum spanning tree over these Steiner nodes and a given set of special nodes has the minimum weight, which is NP-hard. STP includes several important cases. The Steiner tree problem in graphs (GSTP) is one of them. Many heuristics have been proposed for STP, and some of them have proved to be performance guarantee approximation algorithms for this problem. Since evolutionary algorithms (EAs) are general and popular randomized heuristics, it is significant to investigate the performance of EAs for STP. Several empirical investigations have shown that EAs are efficient for STP. However, up to now, there is no theoretical work on the performance of EAs for STP. In this article, we reveal that the (1+1) EA achieves 3/2-approximation ratio for STP in a special class of quasi-bipartite graphs in expected runtime [Formula: see text], where [Formula: see text], [Formula: see text], and [Formula: see text] are, respectively, the number of Steiner nodes, the number of special nodes, and the largest weight among all edges in the input graph. We also show that the (1+1) EA is better than two other heuristics on two GSTP instances, and the (1+1) EA may be inefficient on a constructed GSTP instance.

13

Chen, Junpu, and Hong Xie. "An Online Learning Approach to Sequential User-Centric Selection Problems." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 6 (June 28, 2022): 6231–38. http://dx.doi.org/10.1609/aaai.v36i6.20572.

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This paper proposes a new variant of multi-play MAB model, to capture important factors of the sequential user-centric selection problem arising from mobile edge computing, ridesharing applications, etc. In the proposed model, each arm is associated with discrete units of resources, each play is associate with movement costs and multiple plays can pull the same arm simultaneously. To learn the optimal action profile (an action profile prescribes the arm that each play pulls), there are two challenges: (1) the number of action profiles is large, i.e., M^K, where K and M denote the number of plays and arms respectively; (2) feedbacks on action profiles are not available, but instead feedbacks on some model parameters can be observed. To address the first challenge, we formulate a completed weighted bipartite graph to capture key factors of the offline decision problem with given model parameters. We identify the correspondence between action profiles and a special class of matchings of the graph. We also identify a dominance structure of this class of matchings. This correspondence and dominance structure enable us to design an algorithm named OffOptActPrf to locate the optimal action efficiently. To address the second challenge, we design an OnLinActPrf algorithm. We design estimators for model parameters and use these estimators to design a Quasi-UCB index for each action profile. The OnLinActPrf uses OffOptActPrf as a subroutine to select the action profile with the largest Quasi-UCB index. We conduct extensive experiments to validate the efficiency of OnLinActPrf.

14

Zhao, Pan, Wenlei Guo, Datong Xu, Zhiliang Jiang, Jie Chai, Lijun Sun, He Li, and Weiliang Han. "Hypergraph-based resource allocation for Device-to-Device underlay H-CRAN network." International Journal of Distributed Sensor Networks 16, no. 8 (August 2020): 155014772095133. http://dx.doi.org/10.1177/1550147720951337.

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In the hybrid communication scenario of the Heterogeneous Cloud Radio Access Network and Device-to-Device in 5G, spectrum efficiency promotion and the interference controlling caused by spectrum reuse are still challenges. In this article, a novel resource management method, consisting of power and channel allocation, is proposed to solve this problem. An optimization model to maximum the system throughput and spectrum efficiency of the system, which is constrained by Signal to Interference plus Noise Ratio requirements of all users in diverse layers, is established. To solve the non-convex mixed integer nonlinear optimization problem, the optimization model is decomposed into two sub-problems, which are all solvable quasi-convex power allocation and non-convex channel allocation. The first step is to solve a power allocation problem based on solid geometric programming with the vertex search method. Then, a channel allocation constructed by three-dimensional hypergraph matching is established, and the best result of this problem is obtained by a heuristic greed algorithm based on the bipartite conflict graph and µ-claw search. Finally, the simulation results show that the proposed scheme improves the throughput performance at least 6% over other algorithms.

15

MA, XIAOBIN, and FAN JIANG. "A NOTE ON THE SINGULARITY OF ORIENTED GRAPHS." Bulletin of the Australian Mathematical Society, April 25, 2022, 1–6. http://dx.doi.org/10.1017/s000497272200034x.

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Abstract An oriented graph is called singular or nonsingular according as its adjacency matrix is singular or nonsingular. In this note, by a new approach, we determine the singularity of oriented quasi-trees. The main results of Chen et al. [‘Singularity of oriented graphs from several classes’, Bull. Aust. Math. Soc.102(1) (2020), 7–14] follow as corollaries. Furthermore, we give a necessary condition for an oriented bipartite graph to be nonsingular. By applying this condition, we characterise nonsingular oriented bipartite graphs $B_{m,n}$ when $\min \{m,n\}\leq 3$ .

16

MA, XIAOBIN, and FAN JIANG. "A NOTE ON THE SINGULARITY OF ORIENTED GRAPHS." Bulletin of the Australian Mathematical Society, April 25, 2022, 1–6. http://dx.doi.org/10.1017/s000497272200034x.

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Abstract An oriented graph is called singular or nonsingular according as its adjacency matrix is singular or nonsingular. In this note, by a new approach, we determine the singularity of oriented quasi-trees. The main results of Chen et al. [‘Singularity of oriented graphs from several classes’, Bull. Aust. Math. Soc.102(1) (2020), 7–14] follow as corollaries. Furthermore, we give a necessary condition for an oriented bipartite graph to be nonsingular. By applying this condition, we characterise nonsingular oriented bipartite graphs $B_{m,n}$ when $\min \{m,n\}\leq 3$ .

17

Fernández, Blas, Marija Maksimović, and Sanja Rukavina. "Characterizing Bipartite Distance-Regularized Graphs with Vertices of Eccentricity 4." Bulletin of the Malaysian Mathematical Sciences Society 47, no. 3 (April 29, 2024). http://dx.doi.org/10.1007/s40840-024-01690-8.

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AbstractConsider a bipartite distance-regularized graph $$\Gamma $$ Γ with color partitions Y and $$Y'$$ Y ′ . Notably, all vertices in partition Y (and similarly in $$Y'$$ Y ′ ) exhibit a shared eccentricity denoted as D (and $$D'$$ D ′ , respectively). The characterization of bipartite distance-regularized graphs, specifically those with $$D \le 3$$ D ≤ 3 , in relation to the incidence structures they represent is well established. However, when $$D=4$$ D = 4 , there are only two possible scenarios: either $$D'=3$$ D ′ = 3 or $$D'=4$$ D ′ = 4 . The instance where $$D=4$$ D = 4 and $$D'=3$$ D ′ = 3 has been previously investigated. In this paper, we establish a one-to-one correspondence between the incidence graphs of quasi-symmetric SPBIBDs with parameters $$(v, b, r, k, \lambda _1, 0)$$ ( v , b , r , k , λ 1 , 0 ) of type $$(k-1, t)$$ ( k - 1 , t ) , featuring intersection numbers $$x=0$$ x = 0 and $$y>0$$ y > 0 (where $$y \le t < k$$ y ≤ t < k ), and bipartite distance-regularized graphs with $$D=D'=4$$ D = D ′ = 4 . Moreover, our investigations result in the systematic classification of 2-Y-homogeneous bipartite distance-regularized graphs, which are incidence graphs of quasi-symmetric SPBIBDs with parameters $$(v,b,r,k, \lambda _1,0)$$ ( v , b , r , k , λ 1 , 0 ) of type $$(k-1,t)$$ ( k - 1 , t ) with intersection numbers $$x=0$$ x = 0 and $$y=1$$ y = 1 .

18

Féray, Valentin. "Cyclic inclusion-exclusion and the kernel of P -partitions." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings, 28th... (April 22, 2020). http://dx.doi.org/10.46298/dmtcs.6344.

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International audience Following the lead of Stanley and Gessel, we consider a linear map which associates to an acyclic directed graph (or a poset) a quasi-symmetric function. The latter is naturally defined as multivariate generating series of non-decreasing functions on the graph (or of P -partitions of the poset).We describe the kernel of this linear map, using a simple combinatorial operation that we call cyclic inclusion- exclusion. Our result also holds for the natural non-commutative analog and for the commutative and non-commutative restrictions to bipartite graphs.

19

Kothari, Nishad, Marcelo H. De Carvalho, Cláudio L. Lucchesi, and Charles H. C. Little. "On Essentially 4-Edge-Connected Cubic Bricks." Electronic Journal of Combinatorics 27, no. 1 (January 24, 2020). http://dx.doi.org/10.37236/8594.

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Lovász (1987) proved that every matching covered graph $G$ may be uniquely decomposed into a list of bricks (nonbipartite) and braces (bipartite); we let $b(G)$ denote the number of bricks. An edge $e$ is removable if $G-e$ is also matching covered; furthermore, $e$ is $b$-invariant if $b(G-e)=1$, and $e$ is quasi-$b$-invariant if $b(G-e)=2$. (Each edge of the Petersen graph is quasi-$b$-invariant.) A brick $G$ is near-bipartite if it has a pair of edges $\{e,f\}$ so that $G-e-f$ is matching covered and bipartite; such a pair $\{e,f\}$ is a removable doubleton. (Each of $K_4$ and the triangular prism $\overline{C_6}$ has three removable doubletons.) Carvalho, Lucchesi and Murty (2002) proved a conjecture of Lovász which states that every brick, distinct from $K_4$, $\overline{C_6}$ and the Petersen graph, has a $b$-invariant edge. A cubic graph is essentially $4$-edge-connected if it is $2$-edge-connected and if its only $3$-cuts are the trivial ones; it is well-known that each such graph is either a brick or a brace; we provide a graph-theoretical proof of this fact. We prove that if $G$ is any essentially $4$-edge-connected cubic brick then its edge-set may be partitioned into three (possibly empty) sets: (i) edges that participate in a removable doubleton, (ii) $b$-invariant edges, and (iii) quasi-$b$-invariant edges; our Main Theorem states that if $G$ has two adjacent quasi-$b$-invariant edges, say $e_1$ and $e_2$, then either $G$ is the Petersen graph or the (near-bipartite) Cubeplex graph, or otherwise, each edge of $G$ (distinct from $e_1$ and $e_2$) is $b$-invariant. As a corollary, we deduce that each essentially $4$-edge-connected cubic non-near-bipartite brick $G$, distinct from the Petersen graph, has at least $|V(G)|$ $b$-invariant edges.

20

Polcyn, Joanna. "Large Holes in Quasi-Random Graphs." Electronic Journal of Combinatorics 15, no. 1 (April 18, 2008). http://dx.doi.org/10.37236/784.

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Quasi-random graphs have the property that the densities of almost all pairs of large subsets of vertices are similar, and therefore we cannot expect too large empty or complete bipartite induced subgraphs in these graphs. In this paper we answer the question what is the largest possible size of such subgraphs. As an application, a degree condition that guarantees the connection by short paths in quasi-random pairs is stated.

21

Rizzi, Romeo. "On the Steiner Tree 3/2-Approximation for Quasi-Bipartite Graphs." BRICS Report Series 6, no. 39 (December 9, 1999). http://dx.doi.org/10.7146/brics.v6i39.20108.

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<p>Let G = (V,E) be an undirected simple graph and w : E -> R+ be<br />a non-negative weighting of the edges of G. Assume V is partitioned<br />as R union X. A Steiner tree is any tree T of G such that every node<br />in R is incident with at least one edge of T. The metric Steiner tree<br />problem asks for a Steiner tree of minimum weight, given that w is a<br />metric. When X is a stable set of G, then (G,R,X) is called quasi-bipartite.<br /> In [1], Rajagopalan and Vazirani introduced the notion of<br />quasi-bipartiteness and gave a ( 3/2 + epsilon) approximation algorithm<br /> for the metric Steiner tree problem, when (G,R,X) is quasi-bipartite. In this<br />paper, we simplify and strengthen the result of Rajagopalan and Vazirani.<br />We also show how classical bit scaling techniques can be adapted<br />to the design of approximation algorithms.</p><p>Key words: Steiner tree, local search, approximation algorithm, bit scaling.</p><p> </p>

22

Raeisi, G., and M. Gholami. "On a class of column‐weight 3 decomposable LDPC codes with the analysis of elementary trapping sets." IET Communications, April 22, 2024. http://dx.doi.org/10.1049/cmu2.12762.

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AbstractA column‐weight LDPC code with the parity‐check matrix is called decomposable if there exists a permutation on the rows of , such that can be decomposed into column‐weight one matrix. In this paper, some variations of edge coloring of graphs are used to construct some column‐weight three decomposable LDPC codes with girths at least six and eight. Applying the presented method on several known classes of bipartite graphs, some classes of column‐weight three decomposable LDPC codes are derived having flexibility in length and rate. Interestingly, the constructed parity‐check matrices based on the proper edge coloring of graphs can be considered as the base matrix of some high rate column‐weight three quasi‐cyclic (QC) LDPC codes with maximum‐achievable girth 20. The paper also leads to a simple characterization of elementary trapping sets of the decomposable codes based on the chromatic index of the corresponding normal graphs. This characterization corresponds to a simple search algorithm finds all possible existing elementary trapping sets in a girth‐6 or girth‐8 column‐weight 3 LDPC code which are layered super set of a short cycle in the Tanner graph of the code. Simulation results indicate that the QC‐LDPC codes with large girths lifted from the constructed base matrices have good performances over AWGN channel.

23

Hrgovčić, Hrvoje J. "Brownian-Huygens Propagation: Modeling Wave Functions with Discrete Particle-Antiparticle Random Walks." International Journal of Theoretical Physics 61, no. 9 (September 27, 2022). http://dx.doi.org/10.1007/s10773-022-05217-4.

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AbstractWe present a simple method of discretely modeling solutions of the classical wave and Klein-Gordon equations using variations of random walks on a graph. Consider a collection of particles executing random walks on an undirected bipartite graph embedded in $$\mathbb {R}^{D}$$ R D at discrete times $$\mathbb {Z}$$ Z , and assume those walks are “heat-like”, in the sense that a (conserved) density of particles obeys the heat equation in the continuum limit. If the particles possess a binary degree of freedom (so that they may be said to be either particles or “antiparticles”, i.e., “positive” or “negative), then there exist closely related branching random walks on the same graph that are “wave-like”, in the sense that their (also conserved) net density obeys the D-dimensional classical wave equation. Such wave-like paths can be generated even on random graphs. The transformation by which the heat-like random walks become wave-like branching random walks is as follows: at every time step, any “incoming” particle arriving at any node X of the graph along some edge eX creates a particle-antiparticle pair at that node, with the stipulation that the newly created particle with the opposite sign of the incoming particle must initially step (in “Huygens” back-propagation fashion) along eX in the reverse direction, while the other two take a step (in “Brownian” fashion) along any edge of X (including possibly eX) with equal likelihood, and chosen independently. An additional degree of freedom (resulting in “bra” and “ket” particles) leads to quasi-probability densities proportional to the square of the wave functions.

24

Lozano, Álvaro, Rubén Vigara, Carmen Mayora-Cebollero, and Roberto Barrio. "Dominant patterns in small directed bipartite networks: ubiquitous generalized tripod gait." Nonlinear Dynamics, June 20, 2024. http://dx.doi.org/10.1007/s11071-024-09830-2.

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AbstractThe synchronization patterns exhibited by small networks of neurons that regulate biological processes (CPGs) have aroused growing scientific interest. In many of these networks there is a main behavioral pattern within the parameter space. In particular, in the context of insect locomotion, tripod walking stands out as a predominant pattern, both in natural observations (where insects walk on tripod gait) and in mathematical models. This predominance appears to be stable under parameter variations within the network, suggesting a possible correlation with the underlying network topology. Tripod walking can be naturally extended to all CPGs with a bipartite connectivity. Then a natural question arises: Are “generalized tripod gaits” equally dominant among synchronization patterns within those networks? To investigate this, we carried out a comprehensive study covering all bipartite networks of up to nine neurons. For each of those networks we numerically explore the phase space using a quasi-MonteCarlo method to see what are the main synchronization patterns that the network can achieve. Then, all those patterns are grouped according to their dynamics. Generalized tripod gait was observed in all cases examined as the dominant pattern again. However, certain cases revealed additional stable patterns, mainly associated with the 3-colorings of the respective graph structures.