# Tenacity and some related results

Document Type: Research Paper

Author

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.

Keywords