Tenacity of total graphs

Communication networks must be constructed to be as stable as possible, not only with the respect to the initial disruption, but also with respect to the possible reconstruction. Many graph theoretical parameters have been used to describe the stability of communication networks. Tenacity is a reasonable one, which shows not only the difficulty to break down the network but also the damage that has been caused. Total graphs are the largest graphs formed by the adjacent relations of elements of a graph. Thus, total graphs are highly recommended for the design of interconnection networks. In this paper, we determine the tenacity of the total graph of a path, cycle and complete bipartite graph, and thus give a lower bound of the tenacity for the total graph of a graph.