… the toughness of (spanning) subgraphs of G and related graphs … t, and we study which
subdivisions of 2-connected graphs … We will now prove that if two neighbors u and v with d(u) d(v) …

… neighbor connectivity and toughness, we define edge neighbor toughness(ENT) of a connected
graph … the computation problem of edge neighbor toughness of a graph is N P -complete…

… The toughness indexτ(G) of a graph G is defined to be the largest integer t such … graphs
are exactly those graphs for which τ(G) ≥ 0. In this paper, it is shown that if G is a planar graph, …

… There is only one choice for v up to automorphism in the graph G and this forces two of its
neighbors into S while the other three must be in separate components of G - S. By inspection …

… existed with a partitioning Q ∪ I of its vertex set, where Q spans a clique and I an independent
set, then every vertex of Q would have at most one neighbor in I, but these split graphs …

… As the generalized vertex connectivity is closely related to graph toughness, we also present
a lower bound on the generalized vertex connectivity of ( n , d , λ ) -graphs, which implies …

… for reliability of a graph called the neighbor toughness which is … neighbor toughness we
know that, in general, the more the neighbor toughness of a graph is, the more stable the graph is…

… toughness of a 3-regular graph (except for K4) is at most 3/2 and Jackson and Katerinis gave
a characterization of cubic 3/2-tough graphs and these graphs … at least one neighbor in S, …

… the toughness is small and we determine the exact value of the toughness for many strongly
regular graphs … If S is the neighborhood of some vertex of T v , then T v ∖ S consists of two …

… of Toughness and Tenacity for some special classes of graphs … Toughness and tenacities of
several classes of graphs have … regular graph is a graph where each vertex has 3 neighbors. …