The g-extra connectivity of the Mycielskian
Abstract
The g-extra connectivity is an important parameter to measure the ability of tolerance and reliability of interconnection networks. Given a connected graph G=(V,E) and a non-negative integer g, a subset S⊂eq V is called a g-extra cut of G if G-S is disconnected and every component of G-S has at least g+1 vertices. The cardinality of the minimum g-extra cut is defined as the g-extra connectivity of G, denoted by g(G). In a search for triangle-free graphs with arbitrarily large chromatic numbers, Mycielski developed a graph transformation that transforms a graph G into a new graph μ(G), which is called the Mycielskian of G. This paper investigates the relationship of the g-extra connectivity of the Mycielskian μ(G) and the graph G, moreover, show that 2g+1(μ(G))=2g(G)+1 for g≥ 1 and g(G)≤ min\g+1, n2\.