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Journal articles on the topic 'Degree sum'

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Author: Grafiati

Published: 25 May 2024

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1

Boregowda, H. S., and R. B. Jummannaver. "Neighbors degree sum energy of graphs." Journal of Applied Mathematics and Computing 67, no. 1-2 (January 20, 2021): 579–603. http://dx.doi.org/10.1007/s12190-020-01480-y.

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2

Liu, Ze-meng, and Li-ming Xiong. "Degree sum conditions for hamiltonian index." Applied Mathematics-A Journal of Chinese Universities 36, no. 3 (September 2021): 403–11. http://dx.doi.org/10.1007/s11766-021-3885-4.

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AbstractIn this note, we show a sharp lower bound of $$\min \left\{{\sum\nolimits_{i = 1}^k {{d_G}({u_i}):{u_1}{u_2} \ldots {u_k}}} \right.$$ min { ∑ i = 1 k d G ( u i ) : u 1 u 2 … u k is a path of (2-)connected G on its order such that (k-1)-iterated line graphs Lk−1(G) are hamiltonian.

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3

MacHale, Desmond. "Degree Sum Deficiency in Finite Groups." Mathematical Proceedings of the Royal Irish Academy 115A, no. 1 (2015): 1–11. http://dx.doi.org/10.1353/mpr.2015.0007.

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4

Flandrin, E., H. A. Jung, and H. Li. "Hamiltonism, degree sum and neighborhood intersections." Discrete Mathematics 90, no. 1 (June 1991): 41–52. http://dx.doi.org/10.1016/0012-365x(91)90094-i.

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5

Stephen Buckley, Desmond MacHale, and Áine Ní Shé. "Degree Sum Deficiency in Finite Groups." Mathematical Proceedings of the Royal Irish Academy 115A, no. 1 (2015): 1. http://dx.doi.org/10.3318/pria.2015.115.6.

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6

Mohammed, K. Saleel, and Raji Pilakkat. "Minimum inclusive degree sum dominating set." Malaya Journal of Matematik 8, no. 4 (2020): 1885–89. http://dx.doi.org/10.26637/mjm0804/0091.

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7

Faudree, Jill, Ralph J. Faudree, Ronald J. Gould, Paul Horn, and Michael S. Jacobson. "Degree sum and vertex dominating paths." Journal of Graph Theory 89, no. 3 (April 20, 2018): 250–65. http://dx.doi.org/10.1002/jgt.22249.

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8

Hu, Zhi-quan, and Feng Tian. "On k-ordered Graphs Involved Degree Sum." Acta Mathematicae Applicatae Sinica, English Series 19, no. 1 (March 2003): 97–106. http://dx.doi.org/10.1007/s10255-003-0085-3.

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9

Ferrara, Michael, Michael Jacobson, and Jeffrey Powell. "Characterizing degree-sum maximal nonhamiltonian bipartite graphs." Discrete Mathematics 312, no. 2 (January 2012): 459–61. http://dx.doi.org/10.1016/j.disc.2011.08.029.

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10

Liu, Jianping, Aimei Yu, Keke Wang, and Hong-Jian Lai. "Degree sum and hamiltonian-connected line graphs." Discrete Mathematics 341, no. 5 (May 2018): 1363–79. http://dx.doi.org/10.1016/j.disc.2018.02.008.

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11

B., Basavanagoud, and Chitra E. "Degree square sum equienergetic and hyperenergetic graphs." Malaya Journal of Matematik 8, no. 2 (April 2020): 301–5. http://dx.doi.org/10.26637/mjm0802/0001.

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12

Sharp, Jonathan. "Sum of the parts; my degree course." Electronics Education 1995, no. 1 (1995): 38–40. http://dx.doi.org/10.1049/ee.1995.0022.

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13

Fan, Genghua, and Chuixiang Zhou. "Degree sum and nowhere-zero 3-flows." Discrete Mathematics 308, no. 24 (December 2008): 6233–40. http://dx.doi.org/10.1016/j.disc.2007.11.045.

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14

Hu, Zhiquan, and Hao Li. "Weak cycle partition involving degree sum conditions." Discrete Mathematics 309, no. 4 (March 2009): 647–54. http://dx.doi.org/10.1016/j.disc.2007.12.081.

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15

Mukungunugwa, Vivian, and Simon Mukwembi. "On eccentric distance sum and minimum degree." Discrete Applied Mathematics 175 (October 2014): 55–61. http://dx.doi.org/10.1016/j.dam.2014.05.019.

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16

Ellingham, M. N., Xiaoya Zha, and Yi Zhang. "Spanning 2-trails from degree sum conditions." Journal of Graph Theory 45, no. 4 (2004): 298–319. http://dx.doi.org/10.1002/jgt.10162.

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17

Gurjar, Jeetendra, and Sudhir Raghunath Jog. "Degree Sum Exponent Distance Energy of Some Graphs." Journal of the Indonesian Mathematical Society 27, no. 1 (March 31, 2021): 64–74. http://dx.doi.org/10.22342/jims.27.1.931.64-74.

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The degree sum exponent distance matrix M(G)of a graph G is a square matrix whose (i,j)-th entry is (di+dj)^ d(ij) whenever i not equal to j, otherwise it is zero, where di is the degree of i-th vertex of G and d(ij)=d(vi,vj) is distance between vi and vj. In this paper, we define degree sum exponent distance energy E(G) as sum of absolute eigenvalues of M(G). Also, we obtain some bounds on the degree sum exponent distance energy of some graphs and deduce direct expressions for some graphs.

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18

Akka, Danappa G., G. K. Dayanand, and Shabbir Ahmed. "EDGE DEGREE WEIGHT SUM OF PRODUCTS, SUM(JOIN) AND CORONA OF THREE GRAPHS." Far East Journal of Applied Mathematics 90, no. 1 (March 12, 2015): 1–19. http://dx.doi.org/10.17654/fjamjan2015_001_019.

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19

Basavanagoud, B., and Chitra E. "Degree Square Sum Polynomial of some Special Graphs." International Journal of Applied Engineering Research 13, no. 19 (October 15, 2018): 14060. http://dx.doi.org/10.37622/ijaer/13.19.2018.14060-14078.

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20

Opie, Greg. "Expansion by Degree: The Sum of All Essays." New Writing 4, no. 2 (October 15, 2007): 118–33. http://dx.doi.org/10.2167/new428.0.

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21

Okamura, Haruko, and Tomoki Yamashita. "Degree Sum Conditions for Cyclability in Bipartite Graphs." Graphs and Combinatorics 29, no. 4 (March 17, 2012): 1077–85. http://dx.doi.org/10.1007/s00373-012-1148-0.

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22

Ota, Katsuhiro. "Cycles through prescribed vertices with large degree sum." Discrete Mathematics 145, no. 1-3 (October 1995): 201–10. http://dx.doi.org/10.1016/0012-365x(94)00036-i.

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23

Lv, Sheng-xiang, Meng-da Fu, and Yan-pei Liu. "Up-embeddability of graphs with new degree-sum." Acta Mathematicae Applicatae Sinica, English Series 33, no. 1 (February 2017): 169–74. http://dx.doi.org/10.1007/s10255-017-0647-4.

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24

Chen, Zhi-Hong. "Supereulerian graphs, independent sets, and degree-sum conditions." Discrete Mathematics 179, no. 1-3 (January 1998): 73–87. http://dx.doi.org/10.1016/s0012-365x(97)00028-9.

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25

Malafiejski, Michal, Krzysztof Giaro, Robert Janczewski, and Marek Kubale. "Sum Coloring of Bipartite Graphs with Bounded Degree." Algorithmica 40, no. 4 (August 20, 2004): 235–44. http://dx.doi.org/10.1007/s00453-004-1111-4.

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26

Yang, Fan, and Xiangwen Li. "Degree sum of 3 independent vertices andZ3-connectivity." Discrete Mathematics 313, no. 21 (November 2013): 2493–505. http://dx.doi.org/10.1016/j.disc.2013.07.009.

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27

Gould, Ronald J., Kazuhide Hirohata, and Ariel Keller. "On vertex-disjoint cycles and degree sum conditions." Discrete Mathematics 341, no. 1 (January 2018): 203–12. http://dx.doi.org/10.1016/j.disc.2017.08.030.

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28

Basavanagoud, B., and Anand P. Barangi. "Degree Sum Polynomial Obtained by Some Graph Operators." Journal of Computer and Mathematical Sciences 9, no. 8 (August 6, 2018): 977–1000. http://dx.doi.org/10.29055/jcms/836.

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29

Yamashita, Tomoki. "Degree sum and connectivity conditions for dominating cycles." Discrete Mathematics 308, no. 9 (May 2008): 1620–27. http://dx.doi.org/10.1016/j.disc.2007.04.019.

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30

Qiao, Shengning, and Shenggui Zhang. "Degree sum conditions for oriented forests in digraphs." Discrete Mathematics 309, no. 13 (July 2009): 4642–45. http://dx.doi.org/10.1016/j.disc.2009.01.023.

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31

Zhang, Xiaoxia, Mingquan Zhan, Rui Xu, Yehong Shao, Xiangwen Li, and Hong-Jian Lai. "Degree sum condition for Z3-connectivity in graphs." Discrete Mathematics 310, no. 23 (December 2010): 3390–97. http://dx.doi.org/10.1016/j.disc.2010.08.004.

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32

Fan, Genghua. "Degree sum for a triangle in a graph." Journal of Graph Theory 12, no. 2 (1988): 249–63. http://dx.doi.org/10.1002/jgt.3190120216.

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33

Christopher, A. David. "Remainder sum and quotient sum function." Discrete Mathematics, Algorithms and Applications 07, no. 01 (February 2, 2015): 1550001. http://dx.doi.org/10.1142/s1793830915500019.

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This paper is concerned with two arithmetical functions namely remainder sum function and quotient sum function which are respectively the sequences A004125 and A006218 in Online Encyclopedia of Integer Sequences. The remainder sum function is defined by [Formula: see text] for every positive integer n, and quotient sum function is defined by [Formula: see text] where q(n, i) is the quotient obtained when n is divided by i. We establish few divisibility properties these functions enjoy and we found their bounds. Furthermore, we define restricted remainder sum function by RA(n) = ∑k∈A n mod k where A is a set of positive integers and we define restricted quotient sum function by QA(n) = ∑k∈A q(n, k). The function QA(n) is found to be a quasi-polynomial of degree one when A is a finite set of positive integers and RA(n) is found to be a periodic function with period ∏a∈A a. Finally, the above defined four functions found to have recurrence relation whose derivation requires few results from integer partition theory.

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34

Wang, Shilin, Zhou Bo, and Nenad Trinajstic. "On the sum-connectivity index." Filomat 25, no. 3 (2011): 29–42. http://dx.doi.org/10.2298/fil1103029w.

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The sum-connectivity index of a simple graph G is defined in mathematical chemistry as R+(G) = ? uv?E(G)(du+dv)?1/2, where E(G) is the edge set of G and du is the degree of vertex u in G. We give a best possible lower bound for the sum-connectivity index of a graph (a triangle-free graph, respectively) with n vertices and minimum degree at least two and characterize the extremal graphs, where n ? 11.

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35

Chen, Mei, Mei Zhang, Ming Li, Mingwei Leng, Zhichong Yang, and Xiaofang Wen. "Detecting communities by suspecting the maximum degree nodes." International Journal of Modern Physics B 33, no. 13 (May 20, 2019): 1950133. http://dx.doi.org/10.1142/s0217979219501339.

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Detecting the natural communities in a real-world network can uncover its underlying structure and potential function. In this paper, a novel community algorithm SUM is introduced. The fundamental idea of SUM is that a node with relatively low degree stays faithful to its community, because it only has links with nodes in one community, while a node with relatively high degree not only has links with nodes within but also outside its community, and this may cause confusion when detecting communities. Based on this idea, SUM detects communities by suspecting the links of the maximum degree nodes to their neighbors within a community, and relying mainly on the nodes with relatively low degree simultaneously. SUM elegantly defines a similarity which takes into account both the commonality and the rejective degree of two adjacent nodes. After putting similar nodes into one community, SUM generates initial communities by reassigning the maximum degree nodes. Next, SUM assigns nodes without labels to the initial communities, and adjusts the border node to its most linked community. To evaluate the effectiveness of SUM, SUM is compared with seven baselines, including four classical and three state-of-the-art methods on a wide range of complex networks. On the small size networks with ground-truth community structures, results are visually demonstrated, as well as quantitatively measured with ARI, NMI and Modularity. On the relatively large size networks without ground-truth community structures, the performances of these algorithms are evaluated according to Modularity. Experimental results indicate that SUM can effectively determine community structures on small or relatively large size networks with high quality, and also outperforms the compared state-of-the-art methods.

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36

Laib, Ilias, and Nadir Rezzoug. "On a sum over primitive sequences of finite degree." Mathematica Montisnigri 53 (2022): 26–32. http://dx.doi.org/10.20948/mathmontis-2022-53-4.

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A sequence of strictly positive integers is said to be primitive if none of its terms divides the others and is said to be homogeneous if the number of prime factors of its terms counted with multiplicity is constant. In this paper, we construct primitive sequences A of degree d, for which the Erdős’s analogous conjecture for translated sums is not satisfied.

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37

Nicholson, Emlee W., and Bing Wei. "Degree Sum Condition for k-ordered Hamiltonian Connected Graphs." Graphs and Combinatorics 31, no. 3 (December 24, 2013): 743–55. http://dx.doi.org/10.1007/s00373-013-1393-x.

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38

Elliott, Bradley, Ronald J. Gould, and Kazuhide Hirohata. "On Degree Sum Conditions and Vertex-Disjoint Chorded Cycles." Graphs and Combinatorics 36, no. 6 (September 21, 2020): 1927–45. http://dx.doi.org/10.1007/s00373-020-02227-z.

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39

Yan, Jin, Shaohua Zhang, Yanyan Ren, and Junqing Cai. "Degree sum conditions on two disjoint cycles in graphs." Information Processing Letters 138 (October 2018): 7–11. http://dx.doi.org/10.1016/j.ipl.2018.05.004.

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40

Jiao, Zhihui, Hong Wang, and Jin Yan. "Disjoint cycles in graphs with distance degree sum conditions." Discrete Mathematics 340, no. 6 (June 2017): 1203–9. http://dx.doi.org/10.1016/j.disc.2017.01.013.

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41

Chen, Guantao, Shuya Chiba, Ronald J. Gould, Xiaofeng Gu, Akira Saito, Masao Tsugaki, and Tomoki Yamashita. "Spanning bipartite graphs with high degree sum in graphs." Discrete Mathematics 343, no. 2 (February 2020): 111663. http://dx.doi.org/10.1016/j.disc.2019.111663.

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42

Chen, Guantao, and Michael S. Jacobson. "Degree Sum Conditions for Hamiltonicity on k-Partite Graphs." Graphs and Combinatorics 13, no. 4 (December 1997): 325–43. http://dx.doi.org/10.1007/bf03353011.

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43

Hua, Hongbo, Hongzhuan Wang, and Xiaolan Hu. "On eccentric distance sum and degree distance of graphs." Discrete Applied Mathematics 250 (December 2018): 262–75. http://dx.doi.org/10.1016/j.dam.2018.04.011.

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44

Coll, Vincent E., Colton Magnant, and Pouria Salehi Nowbandegani. "Degree sum and graph linkage with prescribed path lengths." Discrete Applied Mathematics 257 (March 2019): 85–94. http://dx.doi.org/10.1016/j.dam.2018.09.008.

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45

Jiong-Sheng, Li, and Song Zi-Xia. "The smallest degree sum that yields potentiallyPk-graphical sequences." Journal of Graph Theory 29, no. 2 (October 1998): 63–72. http://dx.doi.org/10.1002/(sici)1097-0118(199810)29:2<63::aid-jgt2>3.0.co;2-a.

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46

Beierle, Christof, Alex Biryukov, and Aleksei Udovenko. "On degree-d zero-sum sets of full rank." Cryptography and Communications 12, no. 4 (November 19, 2019): 685–710. http://dx.doi.org/10.1007/s12095-019-00415-0.

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47

DAI, Guowei. "Degree sum and restricted {P2,P5}-factor in graphs." Proceedings of the Romanian Academy, Series A: Mathematics, Physics, Technical Sciences, Information Science 24, no. 2 (June 28, 2023): 105–11. http://dx.doi.org/10.59277/pra-ser.a.24.2.01.

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"For a graph $G$, a spanning subgraph $F$ of $G$ is called a $\{P_2,P_5\}$-factor if every component of $F$ is isomorphic to $P_2$ or $P_5$, where $P_i$ denotes the path of order $i$. A graph $G$ is called a $(\{P_2,P_5\},k)$-factor critical graph if $G-V'$ contains a $\{P_2,P_5\}$-factor for any $V'\subseteq V(G)$ with $|V'|=k$. A graph $G$ is called a $(\{P_2,P_5\},m)$-factor deleted graph if $G-E'$ has a $\{P_2,P_5\}$-factor for any $E'\subseteq E(G)$ with $|E'|=m$. The degree sum of $G$ is defined by $$\sigma_{r+1}(G)=\min_{X\subseteq V(G)}\Big\{\sum_{x\in X}d_G(x): X~\mathrm{is~an~independent~set~of}~r+1~\mathrm{vertices}\Big\}.$$ In this paper, using degree sum conditions, we demonstrate that (i) $G$ is a $(\{P_2,P_5\},k)$-factor critical graph if $\sigma_{r+1}(G)>\frac{(3n+4k-2)(r+1)}{7}$ and $\kappa(G)\geq k+r$; (ii) $G$ is a $(\{P_2,P_5\},m)$-factor deleted graph if $\sigma_{r+1}(G)>\frac{(3n+2m-2)(r+1)}{7}$ and $\kappa(G)\geq\frac{5m}{4}+r$."

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48

Molina, Edil D., Paul Bosch, José M. Sigarreta, and Eva Tourís. "On the variable inverse sum deg index." Mathematical Biosciences and Engineering 20, no. 5 (2023): 8800–8813. http://dx.doi.org/10.3934/mbe.2023387.

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<abstract><p>Several important topological indices studied in mathematical chemistry are expressed in the following way $ \sum_{uv \in E(G)} F(d_u, d_v) $, where $ F $ is a two variable function that satisfies the condition $ F(x, y) = F(y, x) $, $ uv $ denotes an edge of the graph $ G $ and $ d_u $ is the degree of the vertex $ u $. Among them, the variable inverse sum deg index $ IS\!D_a $, with $ F(d_u, d_v) = 1/(d_u^a+d_v^a) $, was found to have several applications. In this paper, we solve some problems posed by Vukičević <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>, and we characterize graphs with maximum and minimum values of the $ IS\!D_a $ index, for $ a < 0 $, in the following sets of graphs with $ n $ vertices: graphs with fixed minimum degree, connected graphs with fixed minimum degree, graphs with fixed maximum degree, and connected graphs with fixed maximum degree. Also, we performed a QSPR analysis to test the predictive power of this index for some physicochemical properties of polyaromatic hydrocarbons.</p></abstract>

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49

Revankar, D. S., Jaishri B. Veeragoudar, and M. M. Patil. "On the degree sum energy of total transformation graphs of regular graphs." Journal of Information & Optimization Sciences 44, no. 2 (2023): 217–29. http://dx.doi.org/10.47974/jios-1220.

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The energy E(G) of a graph G is the sum of absolute values of the eigenvalues of the adjacency matrix of G. This definition of energy was motivated by the large number of results for the Huckel molecular orbital total π-electron energy. Motivated by E(G), The degree sum energy EDS(G) of a simple connected graph G is defined by sum of the absolute values of all eigenvalues of degree sum matrix. In this paper, we obtain spectra and degree sum energy of the total transformation graph Gxyz of a r-regular graph.

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50

GILLOT, VALÉRIE, and PHILIPPE LANGEVIN. "ESTIMATION OF SOME EXPONENTIAL SUM BY MEANS OF q-DEGREE." Glasgow Mathematical Journal 52, no. 2 (March 29, 2010): 315–24. http://dx.doi.org/10.1017/s0017089510000017.

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AbstractIn this paper, we improve results of Gillot, Kumar and Moreno to estimate some exponential sums by means of q-degrees. The method consists in applying suitable elementary transformations to see an exponential sum over a finite field as an exponential sum over a product of subfields in order to apply Deligne bound. In particular, we obtain new results on the spectral amplitude of some monomials.

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