On the edge‐toughness of a graph. II
Y. H. Peng, Tiong-Seng Tay · Journal of Graph Theory · 1993
Abstract The edge‐toughness T1(G) of a graph G is defined as equation image where the minimum is taken over every edge‐cutset X that separates G into ω (G ‐ X) components. We determine this quantity for some special classes of graphs that also gives the arboricity of these graphs. We also give a simpler proof to the following result of Peng et al.: For any positive integers r, s satisfying r/2 < s ≤ r, there exists an infinite family of graphs such that for each graph G in the family, λ(G) = r (where λ(G) is the edge‐connectivity of G) T1(G) = s, and G can be factored into s spanning trees. © 1993 John Wiley & Sons, Inc.