Spectral Conditions, Degree Sequences, and Graphical Properties

Abstract

Integrity, tenacity, binding number, and toughness are significant parameters with which to evaluate network vulnerability and stability. However, we hardly use the definitions of these parameters to evaluate directly. According to the methods, concerning the spectral radius, we show sufficient conditions for a graph to be k-integral, k-tenacious, k-binding, and k-tough, respectively. In this way, the vulnerability and stability of networks can be easier to characterize in the future.