All graphs considered here are finite simple graphs, i.e., graphs without loops, multiple edges or directed edges. For a graph G = (V, E), where V is a vertex set and E is an edge set, we write sometimes V (G) for V and E(G) for E to avoid ambiguity. We shall write G \ v instead of G V \{v} = (V \ {v}, E ∩ 2 V \{v}), the subgraph induced by V \ {v}. A vertex v ∈ V (G) is called a cut-vertex of ...

Given a graph G and an interdiction budget k∈N, the Edge Interdiction Clique Problem (EICP) asks to find subset of at most k edges remove from so that size maximum clique, in interdicted graph, is minimized. The EICP belongs family problems with aim reducing clique number graph. optimal solutions, called policies, determine vital which are crucial for preserving its number. We propose new set-c...

Let G = (V,E) be a connected graph. G is said to be super edge connected (or super-k for short) if every minimum edge cut of G isolates one of the vertex of G. A graph G is called m-super-k if for any edge set S # E(G) with jSj 6m, G S is still super-k. The maximum cardinality of m-super-k is called the edge fault tolerance of super edge connectivity of G. In this paper, we discuss the edge fau...