Integrity of Total Graphs via Certain Parameters

Communication networks have been characterized by high levels of service reliability. Links cuts, node interruptions, software errors or hardware failures, and transmission failures at various points can interrupt service for long periods of time. In communication networks, greater degrees of stability or less vulnerability is required. The vulnerability of communication network measures the resistance of the network to the disruption of operation after the failure of certain stations or communication links. If we think of a graph $G$ as modeling a network, many graph-theoretic parameters can be used to describe the stability of communication networks, including connectivity, integrity, and tenacity. We consider two graphs with the same connectivity, but with unequal orders of theirs largest components. Then these two graphs must be different in respect to stability. How can we measure that property? The idea behind the answer is the concept of integrity, which is different from connectivity. Total graphs constitute a large class of graphs. In this paper, we study the integrity of total graphs via some graph parameters.