Document Type : Research Paper


University of Tehran, College of Engineering, Department of Engineering Science


In this paper we discuss about tenacity and its properties in stability calculation. We indicate relationships between tenacity and connectivity, tenacity and binding number, tenacity and toughness. We also give good lower and upper bounds for tenacity. Since we are primarily interested in the case where disruption of the graph is caused by the removal of a vertex or vertices (and the resulting loss of all edges incident with the removed vertices), we shall restrict our discussion to vertex stability measures. In the interest of completeness, however, we have included several related measures of edge stability.


Received 3, March 2017

Received in revised form 18,

November 2017

Accepted 30, November 2017

Available online 15, December