A New Lower Bound for the Domination Number of Complete Cylindrical Grid Graphs

TL;DR

This paper introduces a new lower bound for the domination number of complete cylindrical grid graphs, using a dynamic programming approach to analyze large instances of these graphs.

Contribution

The paper presents a novel lower bound for the domination number of $C_n imes P_m$ graphs, advancing understanding of domination in cylindrical grid structures.

Findings

Established a new lower bound for large $C_n imes P_m$ graphs.

Demonstrated the effectiveness of dynamic programming in graph domination problems.

Provides insights applicable to related grid graph domination challenges.

Abstract

We use a dynamic programming algorithm to establish a lower bound on the domination number of complete grid graphs of the form $C_n\square P_m$, that is, the Cartesian product of a cycle $C_n$ and a path $P_m$, for $m$ and $n$ sufficiently large.