^{}University of Tehran, College of Engineering, Department of Engineerng Science

Abstract

Conceptually graph vulnerability relates to the study of graph intactness when some of its elements are removed. The motivation for studying vulnerability measures is derived from design and analysis of networks under hostile environment. Graph tenacity has been an active area of research since the the concept was introduced in 1992. The tenacity T(G) of a graph G is defined as \begin{center} $T(G)=\displaystyle \min_{A\subset V(G)}\{\frac{\mid A\mid +\tau(G-A)}{\omega(G-A)}\}$ \end{center} where $\tau(G-A)$ denotes the order (the number of vertices) of a largest component of G-A and $\omega(G-A)$ is the number of components of G-A. In this paper we discuss tenacity and its properties in vulnerability calculation.