Toughness condition for a graph to be all fractional (g,f,n)-critical deleted

Abstract

In data transmission networks, the feasibility of data transmission can be characterized by the existence of fractional factors. If some channels and stations are not available in the transmission network at the moment, the possibility of transmission between data is characterized by whether the corresponding graph structure of the network is critical deleted. Toughness used to measure the vulnerability and robustness of a network, which is an important parameter to be considered in network designing. In this paper, we mainly study the relationship between toughness and the all fractional critical deleted graph, and a toughness condition for a graph to be all fractional (g,f,n)-critical deleted is determined.