Global Clustering Coefficient of the Join and Corona of Graphs

Remarl Joseph M. Damalerio *

Mathematics Department, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon-8714, Philipines.

Rolito G. Eballe

Mathematics Department, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon-8714, Philipines.

Cherry Mae R. Balingit

Mathematics Department, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon-8714, Philipines.

Isagani S. Cabahug Jr.

Mathematics Department, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon-8714, Philipines.

Ann Leslie V. Flores

Mathematics Department, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon-8714, Philipines.

*Author to whom correspondence should be addressed.


Abstract

The global clustering coefficient is one of the most useful indices in complex network analysis. It is another metric that somehow measures how close a graph from being a complete graph. In this paper we present some expressions for the global clustering coefficient of the join G v H and corona G o H of arbitrary simple and undirected graphs G and H. As corollaries to these results, we will show that for the path Pm, cycle Cm, fan Fm, and wheel Wm, both Cc(Pm v Pm) and Cc(Cm v Cm) approach to 0 as m increases without bound, while Cc(Fm), Cc(Wm), Cc(Pm o Pm), and Cc(Cm o Cm) all approach to 2/3.

Keywords: Clustering coefficient, join, vertex corona


How to Cite

Damalerio, R. J. M., Eballe, R. G., Balingit, C. M. R., Cabahug Jr., I. S., & Flores, A. L. V. (2022). Global Clustering Coefficient of the Join and Corona of Graphs. Asian Research Journal of Mathematics, 18(12), 128–140. https://doi.org/10.9734/arjom/2022/v18i12632

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