Vertex cover number in diverse graph architectures

¹ Department of Mathematics, Rajalakshmi Institute of Technology, Chennai 600124, India
² Department of Mathematics for Excellence, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, India
³ Department of Mathematics, Hindustan Institute of Technology and Science, Chennai 603103, India
⁴ School of Physics, Damghan University, Damghan 3671641167, Iran

^* Corresponding author: vprsundar@gmail.com

Received: 28 December 2023
Accepted: 23 December 2024

Abstract

Finding a minimum-sized set of vertices in a graph such that each edge in the graph is incident to at least one vertex in the set is the objective of the study of vertex cover problem. Mathematically, a vertex cover of a graph G is a set S of vertices in G such that every edge of G has at least one end vertex in S. The vertex covering number denoted by β(G) is the minimum cardinality taken over all vertex covering sets of G. In this paper, we obtain the vertex cover number of certain architectures such as hypertrees, glued trees, triangular graphs, and honeycomb rectangular torus.