An isolated toughness condition for graphs to be fractional (k, m)-deleted graphs

Abstract

Let i(G) be the number of isolated vertices in a graph G. As an important parameter in computer networks which measures the vulnerability of network, isolated toughness of graph G is defines as 1(G) = {equation presented} if G is not complete; otherwise, 1(G) = ∞. In this paper, we study the relationship between isolated toughness and fractional (k, m)-deleted graphs and determine that G is a fractional (k, m)-deleted graph if I(G) > k + mk. At last, we propose an open problem for the future studying. © 2017 Utilitas Mathematica Publishing Inc.. All rights reserved.