The Connectivity and Fault Diameter of Strong Product Graph of n Paths

Fault diameter is an important parameter to measure the reliability and efficiency of interconnection networks. Strong product is an efficient method to construct large graphs from small graphs. In this paper, we study the fault diameter of strong product graph of [Formula: see text] paths. By recursion and mathematical induction, combined with the connectivity of the strong product graph of complete graph and connected graph, the connectivity of the strong product graph of [Formula: see text] paths is determined. By defining two [Formula: see text]-dimensional vectors [Formula: see text] and [Formula: see text] to construct internally vertex disjoint paths between any two vertices, the fault diameter of the strong product graph of [Formula: see text] paths is determined.