Clustering Coefficient of the Tensor Product of Graphs
Remarl Joseph M. Damalerio *
Department of Mathematics, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon-8714, Philippines.
Rolito G. Eballe
Department of Mathematics, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon-8714, Philippines.
*Author to whom correspondence should be addressed.
Abstract
Clustering coefficient is one of the most useful indices in complex networks. However, graph theoretic properties of this metric have not been discussed much in the literature, especially in graphs resulting from some binary operations. In this paper we present some expressions for the clustering coefficient of the tensor product of arbitrary graphs, regular graphs, and strongly regular graphs. A Vizing-type upperbound and a sharp lower bound for the clustering coefficient of the tensor product of graphs are also given.
Keywords: Clustering coefficient, tensor product of graphs, regular graphs