Abstract

Graph operations have been extensively applied to the analysis of complex networks with properties abstracted from the real world. The resistance distance is a distance function which is related to the hitting time and random walks on graphs. In this paper, we focus on the resistance distance of a Q-vertex (or edge) join operation G1〈v〉G2 (or G1〈e〉G2) of graphs G1 and G2. When G1 is a regular graph, we give the resistance distance of the Q-vertex (or edge) join graph in terms of the number of walks in G1〈v〉G2 (or G1〈e〉G2).

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