On the Maximum Induced Matching Number of a Stacked-book graph

TL;DR

This paper investigates the maximum induced matching number of stacked-book graphs, formed by the Cartesian product of a star and a path, providing insights into their structural properties.

Contribution

It determines the induced matching number for stacked-book graphs, a new class formed by the Cartesian product of star and path graphs.

Findings

Derived the induced matching number for Gm,n

Provided formulas for specific graph parameters

Enhanced understanding of stacked-book graph structure

Abstract

Suppose that G is a simple, undirected graph. An induced matching in G is a set of edges M in the edge set E(G) of G such that if e1, e2 in M, then no endpoint v1, v2 of e1 and e2 respectively is incident to any edge ek in E(G) such that ek is incident to any edge in M. Denoted by im(G), the maximum cardinal number of M is known as the induced matching number of G. In this work, we probe im(G) where G = Gm,n, which is the stacked-book graph obtained by the Cartesian product of the star graph Sm and path Pn.