Minimum Tenacity of Toroidal graphs

Document Type : Research Paper


University of Tehran, College of Engineering, School of Civil Engineering


The tenacity of a graph G, T(G), is de ned by T(G) = min{[|S|+τ(G-S)]/[ω(G-S)]}, where the minimum is taken over all vertex cutsets S of G. We de ne 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.