Minimum Tenacity of Toroidal graphs
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Abstract:
The tenacity of a graph G, T(G), is dened by T(G) = min{[|S|+τ(G-S)]/[ω(G-S)]}, where the minimum is taken over all vertex cutsets S of G. We dene τ(G - S) to be the number of the vertices in the largest component of the graph G - S, and ω(G - S) be the number of components of G - S.In this paper a lower bound for the tenacity T(G) of a graph with genus γ(G) is obtained using the graph's connectivity κ(G). Then we show that such a bound for almost all toroidal graphs is best possible.
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Journal title
volume 47 issue 1
pages 127- 135
publication date 2016-05-21
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