Parameters and fractional factors in different settings

Abstract

In computer networks, the feasibility of data transmission can be measured in terms of fractional factor model, and specifically the framework of fractional critical deleted graph can express the setting when certain sites and channels are unavailable at a special time. We study the relationship between some parameters in graphs and the existence of fractional (g, f )-factor in various settings here. Our main contributions are three-fold: first, a connectivity condition for a graph to be fractional (g, f , n , m)-critical deleted is determined; second, the relationship between independence number and fractional ID-(g, f , m)-deleted graphs is studied; third, an isolated toughness bound for fractional (g, f )-factors is given in balanced bipartite graph setting. Furthermore, by showing counterexamples we explain that bounds for parameters are tight in some sense, and corresponding conditions in all fractional factor settings are discussed as well. Finally, two open problems are proposed for future research. MSC: 05C70