CLIQUE CENTRALITY AND GLOBAL CLIQUE CENTRALITY IN THE JOIN AND CORONA OF GRAPHS

Abstract

Let $G=(V(G), E(G))$ be a finite, nondirected, simple graph of order n. A nonempty subset $W$ of $V(G)$ such that the subgraph $\langle W\rangle_G$ induced by $W$ is complete is referred to as a clique in $G$. It is considered maximal if it is not properly contained within a larger clique. The size of the largest clique containing $u \in V(G)$ is called the clique centrality of $u$ and is denoted by $\omega_G(u)$. The ratio of the sum of the clique centralities of $G$ at the vertex level to the square of the order of $G$ is called the global clique centrality of $G$, denoted by $\hat{\omega}(G)$. In this paper, we study further the concept of clique centrality and global clique centrality of a graph and investigate it for graphs resulting from some binary operations. In particular, the clique centralities of the vertices in the join and vertex corona of graphs are examined and the corresponding global clique centralities of these graphs are obtained.

Received: February 3, 2023;
Revised: March 21, 2023;