University of TehranJournal of Algorithms and Computation2476-277649120170601Tenacity and some related results83917986ENDaraMoazzamiUniversity of Tehran, College of Engineering, Department of Engineerng ScienceJournal Article20160630Conceptually graph vulnerability relates to the study of graph<br />intactness when some of its elements are removed. The motivation for<br />studying vulnerability measures is derived from design and analysis<br />of networks under hostile environment. Graph tenacity has been an<br />active area of research since the the concept was introduced in<br />1992. <br />The tenacity T(G) of a graph G is defined as<br />begin{center}<br /> $T(G)=displaystyle min_{Asubset V(G)}{frac{mid Amid<br /> +tau(G-A)}{omega(G-A)}}$<br />end{center}<br />where $tau(G-A)$ denotes the order (the number of vertices) of a<br />largest component of G-A and $omega(G-A)$ is the number of<br />components of G-A. <br />In this paper we discuss tenacity and its properties in<br />vulnerability calculation.https://jac.ut.ac.ir/article_7986_4ca995acf8ce801abe8eb3b4123a284c.pdf