The Domination Number of $C_n\square P_m$ for $n\equiv 2\pmod{5}$

TL;DR

This paper precisely determines the domination number of certain cylindrical grid graphs by developing a dynamic programming approach to establish tight bounds, filling a gap in graph theory knowledge.

Contribution

It introduces a dynamic programming method to exactly compute the domination number of $C_n imes P_m$ graphs for specific $n$, providing new bounds and exact values.

Findings

Exact domination number for $C_n imes P_m$ when $n ot ot ext{mod } 5$

New lower and upper bounds matching for these graphs

Method applicable to similar graph classes

Abstract

We use a dynamic programming algorithm to establish a new lower bound on the domination number of complete cylindrical grid graphs of the form $C_n\square P_m$, that is, the Cartesian product of a path and a cycle, when $n\equiv 2\pmod{5}$, and we establish a new upper bound equal to the lower bound, thus computing the exact domination number for these graphs.