Relevant bibliographies by topics / Hamilton-connectivity

Academic literature on the topic 'Hamilton-connectivity'

Author: Grafiati
Published: 25 May 2024

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Journal articles on the topic "Hamilton-connectivity"

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Hayat, Sakander, Asad Khan, Suliman Khan, and Jia-Bao Liu. "Hamilton Connectivity of Convex Polytopes with Applications to Their Detour Index." Complexity 2021 (January 23, 2021): 1–23. http://dx.doi.org/10.1155/2021/6684784.

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A connected graph is called Hamilton-connected if there exists a Hamiltonian path between any pair of its vertices. Determining whether a graph is Hamilton-connected is an NP-complete problem. Hamiltonian and Hamilton-connected graphs have diverse applications in computer science and electrical engineering. The detour index of a graph is defined to be the sum of lengths of detours between all the unordered pairs of vertices. The detour index has diverse applications in chemistry. Computing the detour index for a graph is also an NP-complete problem. In this paper, we study the Hamilton-connectivity of convex polytopes. We construct three infinite families of convex polytopes and show that they are Hamilton-connected. An infinite family of non-Hamilton-connected convex polytopes is also constructed, which, in turn, shows that not all convex polytopes are Hamilton-connected. By using Hamilton connectivity of these families of graphs, we compute exact analytical formulas of their detour index.
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Hayat, Sakander, Muhammad Yasir Hayat Malik, Ali Ahmad, Suliman Khan, Faisal Yousafzai, and Roslan Hasni. "On Hamilton-Connectivity and Detour Index of Certain Families of Convex Polytopes." Mathematical Problems in Engineering 2021 (July 17, 2021): 1–18. http://dx.doi.org/10.1155/2021/5553216.

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A convex polytope is the convex hull of a finite set of points in the Euclidean space ℝ n . By preserving the adjacency-incidence relation between vertices of a polytope, its structural graph is constructed. A graph is called Hamilton-connected if there exists at least one Hamiltonian path between any of its two vertices. The detour index is defined to be the sum of the lengths of longest distances, i.e., detours between vertices in a graph. Hamiltonian and Hamilton-connected graphs have diverse applications in computer science and electrical engineering, whereas the detour index has important applications in chemistry. Checking whether a graph is Hamilton-connected and computing the detour index of an arbitrary graph are both NP-complete problems. In this paper, we study these problems simultaneously for certain families of convex polytopes. We construct two infinite families of Hamilton-connected convex polytopes. Hamilton-connectivity is shown by constructing Hamiltonian paths between any pair of vertices. We then use the Hamilton-connectivity to compute the detour index of these families. A family of non-Hamilton-connected convex polytopes has also been constructed to show that not all convex polytope families are Hamilton-connected.
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Alspach, Brian, and Jiping Liu. "On the Hamilton connectivity of generalized Petersen graphs." Discrete Mathematics 309, no. 17 (September 2009): 5461–73. http://dx.doi.org/10.1016/j.disc.2008.12.016.

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Fan, Jianxi. "Hamilton-connectivity and cycle-embedding of the Möbius cubes." Information Processing Letters 82, no. 2 (April 2002): 113–17. http://dx.doi.org/10.1016/s0020-0190(01)00256-3.

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Hu, Zhiquan, Feng Tian, and Bing Wei. "Hamilton connectivity of line graphs and claw-free graphs." Journal of Graph Theory 50, no. 2 (2005): 130–41. http://dx.doi.org/10.1002/jgt.20099.

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Chen, Yaojun, Feng Tian, and Bing Wei. "Hamilton-connectivity of 3-domination-critical graphs with α⩽δ." Discrete Mathematics 271, no. 1-3 (September 2003): 1–12. http://dx.doi.org/10.1016/s0012-365x(02)00876-2.

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Liao, Lifang, Liulu Zhang, Jun Lv, Yingchun Liu, Jiliang Fang, Peijing Rong, and Yong Liu. "Transcutaneous Electrical Cranial-Auricular Acupoint Stimulation Modulating the Brain Functional Connectivity of Mild-to-Moderate Major Depressive Disorder: An fMRI Study Based on Independent Component Analysis." Brain Sciences 13, no. 2 (February 6, 2023): 274. http://dx.doi.org/10.3390/brainsci13020274.

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Evidence has shown the roles of taVNS and TECS in improving depression but few studies have explored their synergistic effects on MDD. Therefore, the treatment responsivity and neurological effects of TECAS were investigated and compared to escitalopram, a commonly used medication for depression. Fifty patients with mild-to-moderate MDD (29 in the TECAS group and 21 in another) and 49 demographically matched healthy controls were recruited. After an eight-week treatment, the outcomes of TECAS and escitalopram were evaluated by the effective rate and reduction rate based on the Montgomery–Asberg Depression Rating Scale, Hamilton Depression Rating Scale, and Hamilton Anxiety Rating Scale. Altered brain networks were analyzed between pre- and post-treatment using independent component analysis. There was no significant difference in clinical scales between TECAS and escitalopram but these were significantly decreased after each treatment. Both treatments modulated connectivity of the default mode network (DMN), dorsal attention network (DAN), right frontoparietal network (RFPN), and primary visual network (PVN), and the decreased PVN–RFPN connectivity might be the common brain mechanism. However, there was increased DMN–RFPN and DMN–DAN connectivity after TECAS, while it decreased in escitalopram. In conclusion, TECAS could relieve symptoms of depression similarly to escitalopram but induces different changes in brain networks.
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Liu, Donglin, Chunxiang Wang, and Shaohui Wang. "Hamilton-connectivity of Interconnection Networks Modeled by a Product of Graphs." Applied Mathematics and Nonlinear Sciences 3, no. 2 (December 7, 2018): 419–26. http://dx.doi.org/10.21042/amns.2018.2.00032.

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AbstractThe product graph Gm *Gp of two given graphs Gm and Gp, defined by J.C. Bermond et al.[J Combin Theory, Series B 36(1984) 32-48] in the context of the so-called (Δ,D)-problem, is one interesting model in the design of large reliable networks. This work deals with sufficient conditions that guarantee these product graphs to be hamiltonian-connected. Moreover, we state product graphs for which provide panconnectivity of interconnection networks modeled by a product of graphs with faulty elements.
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Chen, Yaojun, Feng Tian, and Yunqing Zhang. "Hamilton-connectivity of 3-Domination Critical Graphs with α=δ+ 2." European Journal of Combinatorics 23, no. 7 (October 2002): 777–84. http://dx.doi.org/10.1006/eujc.2002.0603.

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Nikoghosyan, Zh G. "Disconnected Forbidden Subgraphs, Toughness and Hamilton Cycles." ISRN Combinatorics 2013 (March 10, 2013): 1–4. http://dx.doi.org/10.1155/2013/673971.

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In 1974, Goodman and Hedetniemi proved that every 2-connected -free graph is hamiltonian. This result gave rise many other conditions for Hamilton cycles concerning various pairs and triples of forbidden connected subgraphs under additional connectivity conditions. In this paper we investigate analogous problems when forbidden subgraphs are disconnected which affects more global structures in graphs such as tough structures instead of traditional connectivity structures. In 1997, it was proved that a single forbidden connected subgraph in 2-connected graphs can create only a trivial class of hamiltonian graphs (complete graphs) with . In this paper we prove that a single forbidden subgraph can create a non trivial class of hamiltonian graphs if is disconnected: every -free graph either is hamiltonian or belongs to a well defined class of non hamiltonian graphs; every 1-tough -free graph is hamiltonian. We conjecture that every 1-tough -free graph is hamiltonian and every 1-tough -free graph is hamiltonian.
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Dissertations / Theses on the topic "Hamilton-connectivity"

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Bard, Stefan. "Gray code numbers of complete multipartite graphs." Thesis, 2014. http://hdl.handle.net/1828/5815.

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Let G be a graph and k be an integer greater than or equal to the chromatic number of G. The k-colouring graph of G is the graph whose vertices are k-colourings of G, with two colourings adjacent if they colour exactly one vertex differently. We explore the Hamiltonicity and connectivity of such graphs, with particular focus on the k-colouring graphs of complete multipartite graphs. We determine the connectivity of the k-colouring graph of the complete graph on n vertices for all n, and show that the k-colouring graph of a complete multipartite graph K is 2-connected whenever k is at least the chromatic number of K plus one. Additionally, we examine a conjecture that every connected k-colouring graph is 2-connected, and give counterexamples for k greater than or equal to 4. As our main result, we show that for all k greater than or equal to 2t, the k-colouring graph of a complete t-partite graph is Hamiltonian. Finally, we characterize the complete multipartite graphs K whose k-colouring graphs are Hamiltonian when k is the chromatic number of K plus one.
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Book chapters on the topic "Hamilton-connectivity"

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Broersma, Hajo, Jiří Fiala, Petr A. Golovach, Tomáš Kaiser, Daniël Paulusma, and Andrzej Proskurowski. "Linear-Time Algorithms for Scattering Number and Hamilton-Connectivity of Interval Graphs." In Graph-Theoretic Concepts in Computer Science, 127–38. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-45043-3_12.

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