An Improved Bound for Upper Domination of Cartesian Products of Graphs

Abstract

In this paper, we prove a problem proposed by Brešar: for any graphs $G$ and $H$, $\Gamma (G\square H)\ge \Gamma (G)\Gamma (H)+\min \{|V(G)|-\Gamma (G),|V(H)|-\Gamma (H)\}$, where $\Gamma (G)$ denotes the upper domination number of $G$.

Cited by in corpus (1)

• Tightness of Paired and Upper Domination Inequalities for Direct Product Graphs