An upper bound of the basis number of the strong product of graphs

Mohammed M.M. Jaradat

Displaying similar documents to “An upper bound of the basis number of the strong product of graphs”

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Maciej Sysło (1982)

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The basis number of some special non-planar graphs

Salar Y. Alsardary, Ali A. Ali (2003)

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The basis number of a graph $G$ was defined by Schmeichel to be the least integer $h$ such that $G$ has an $h$ -fold basis for its cycle space. He proved that for $m, n \geq 5$ , the basis number $b (K_{m, n})$ of the complete bipartite graph $K_{m, n}$ is equal to 4 except for $K_{6, 10}$ , $K_{5, n}$ and $K_{6, n}$ with $n = 5, 6, 7, 8$ . We determine the basis number of some particular non-planar graphs such as $K_{5, n}$ and $K_{6, n}$ , $n = 5, 6, 7, 8$ , and $r$ -cages for $r = 5, 6, 7, 8$ , and the Robertson graph.

Voltage graphs, group presentations and cages.

Exoo, Geoffrey (2004)

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The cycle-complete graph Ramsey number r(C₅,K₇)

Ingo Schiermeyer (2005)

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The cycle-complete graph Ramsey number r(Cₘ,Kₙ) is the smallest integer N such that every graph G of order N contains a cycle Cₘ on m vertices or has independence number α(G) ≥ n. It has been conjectured by Erdős, Faudree, Rousseau and Schelp that r(Cₘ,Kₙ) = (m-1)(n-1)+1 for all m ≥ n ≥ 3 (except r(C₃,K₃) = 6). This conjecture holds for 3 ≤ n ≤ 6. In this paper we will present a proof for r(C₅,K₇) = 25.

Characterization of a signed graph whose signed line graph is $S$ -consistent.

Acharya, B.Devadas, Acharya, Mukti, Sinha, Deepa (2009)

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A note on signed cycle domination in graphs

Hossein Karami, Rana Khoeilar, Seyed Mahmoud Sheikholeslami (2013)

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The maximum genus, matchings and the cycle space of a graph

Hung-Lin Fu, Martin Škoviera, Ming-Chun Tsai (1998)

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In this paper we determine the maximum genus of a graph by using the matching number of the intersection graph of a basis of its cycle space. Our result is a common generalization of a theorem of Glukhov and a theorem of Nebeský .

Minimal cycle bases of outerplanar graphs.

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