The 2-good-neighbor connectivity of wheel graph networks

Connectivity is an important measurement for the fault tolerant in interconnection network. A new measure for fault diagnosis of the system is called the g-good-neighbor connectivity is proposed. A fault set F subset of V is called a g-good-neighbor faulty set if vertical bar N(v) boolean AND (V\F)I >= g for every vertex v in V\F. A g-good-neighbor cut of a graph G is a g-good-neighbor faulty set F such that G-F is disconnected. The minimum cardinality of g-good-neighbor cuts is said to be the g-good-neighbor connectivity of G, denoted by kappa((g)) (G). As a famous topology structure of interconnection networks, the n-dimensional wheel graph network CWn has many good properties. In this paper, we prove that the 2-good-neighbor connectivity of CWn is 8n - 18 for n >= 5.