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Relevant bibliographies by topics / K - connected graphs

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Journal articles

Academic literature on the topic 'K - connected graphs'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "K - connected graphs"

1

CHENG, EDDIE, and MARC J. LIPMAN. "UNIDIRECTIONAL (n, k)-STAR GRAPHS." Journal of Interconnection Networks 03, no. 01n02 (2002): 19–34. http://dx.doi.org/10.1142/s0219265902000525.

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Arrangement graphs14 and (n, k)-star graphs11 were introduced as generalizations of star graphs1. They were introduced to provide a wider set of choices for the order of topologically attractive interconnection networks. Unidirectional interconnection networks are more appropriate in many applications. Cheng and Lipman5, and Day and Tripathi17 studied the unidirectional star graphs, and Cheng and Lipman7 studied orientation of arrangement graphs. In this paper, we show that every (n, k)-star graph can be oriented to a maximally arc-connected graph when the regularity of the graph is even. If the regularity is odd, then the resulting directed graph can be augmented to a maximally arc-connected directed graph by adding a directed matching. In either case, the diameter of the resulting directed graph is small. Moreover, there exists a simple and near-optimal routing algorithm.

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2

Ando, Kiyoshi, and Yoko Usami. "Critically (k, k)-connected graphs." Discrete Mathematics 66, no. 1-2 (1987): 15–20. http://dx.doi.org/10.1016/0012-365x(87)90114-2.

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3

Marhelina, Sally. "RAINBOW CONNECTION PADA GRAF k -CONNECTED UNTUK k = 1 ATAU 2." Jurnal Matematika UNAND 2, no. 1 (2013): 78. http://dx.doi.org/10.25077/jmu.2.1.78-84.2013.

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An edge-colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of aconnected graph G, denoted by rc(G) is the smallest number of colors needed such thatG is rainbow connected. In this paper, we will proved again that rc(G) ≤ 3(n + 1)/5 forall 3-connected graphs, and rc(G) ≤ 2n/3 for all 2-connected graphs.

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4

Mynhardt, C. M., L. E. Teshima, and A. Roux. "Connected k-dominating graphs." Discrete Mathematics 342, no. 1 (2019): 145–51. http://dx.doi.org/10.1016/j.disc.2018.09.006.

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5

Hong, Zhen-Mu, Zheng-Jiang Xia, Fuyuan Chen, and Lutz Volkmann. "Sufficient Conditions for Graphs to Be k -Connected, Maximally Connected, and Super-Connected." Complexity 2021 (February 22, 2021): 1–11. http://dx.doi.org/10.1155/2021/5588146.

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Let G be a connected graph with minimum degree δ G and vertex-connectivity κ G . The graph G is k -connected if κ G ≥ k , maximally connected if κ G = δ G , and super-connected if every minimum vertex-cut isolates a vertex of minimum degree. In this paper, we present sufficient conditions for a graph with given minimum degree to be k -connected, maximally connected, or super-connected in terms of the number of edges, the spectral radius of the graph, and its complement, respectively. Analogous results for triangle-free graphs with given minimum degree to be k -connected, maximally connected, or super-connected are also presented.

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6

Hennayake, Kamal, Hong-Jian Lai, Deying Li, and Jingzhong Mao. "Minimally (k, k)-edge-connected graphs." Journal of Graph Theory 44, no. 2 (2003): 116–31. http://dx.doi.org/10.1002/jgt.10132.

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7

Shen, Yuanyuan, Xinhui An, and Baonyindureng Wu. "Hamilton-Connected Mycielski Graphs∗." Discrete Dynamics in Nature and Society 2021 (September 15, 2021): 1–7. http://dx.doi.org/10.1155/2021/3376981.

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Jarnicki, Myrvold, Saltzman, and Wagon conjectured that if G is Hamilton-connected and not K 2 , then its Mycielski graph μ G is Hamilton-connected. In this paper, we confirm that the conjecture is true for three families of graphs: the graphs G with δ G > V G / 2 , generalized Petersen graphs G P n , 2 and G P n , 3 , and the cubes G 3 . In addition, if G is pancyclic, then μ G is pancyclic.

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8

Karpov, D. V. "Blocks in k-connected graphs." Journal of Mathematical Sciences 126, no. 3 (2005): 1167–81. http://dx.doi.org/10.1007/s10958-005-0084-4.

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9

Egawa, Yoshimi. "k-shredders ink-connected graphs." Journal of Graph Theory 59, no. 3 (2008): 239–59. http://dx.doi.org/10.1002/jgt.20336.

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10

Devillers, Alice, Joanna B. Fawcett, Cheryl E. Praeger, and Jin-Xin Zhou. "On k-connected-homogeneous graphs." Journal of Combinatorial Theory, Series A 173 (July 2020): 105234. http://dx.doi.org/10.1016/j.jcta.2020.105234.

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