Global Clustering Coefficient of the Products of Complete 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
The global clustering Coefficient Cc(G) of a connected graph G of order at least 3 is a metric that somehow measures how close G to being a complete graph. Its value ranges from 0 to 1. In this paper, we will show that for the tensor product Km ⊗ Km and cartesian product Km ʘ Km Cc(Km⊗Km) and Cc(Km ʘ Km ) approach to 1 and 1=2, respectively, as m → ∞.
Keywords: Clustering coefficient, tensor product, cartesian product, regular graphs