The decycling number of $P_{m} \square P_{n}^{\ast}$

Abstract

A set of vertices of a graph whose removal leaves an acyclic graph is called a decycling set of the graph. The minimum size of a decycling set of a graph G is referred to as the decycling number of G, denoted by ∇(G). In this paper, we study the decycling number of the Cartesian product of two paths, ∇(Pm□Pn), and obtain several new results. Mainly, we prove that [Formula: see text]. Moreover, we obtain the exact value of ∇(Pm□Pn) for some classes (modulo 6) of pairs (m, n).