Vizing-like Conjecture for the Upper Domination of Cartesian Products of Graphs – The Proof

Author:

Brešar Boštjan

Abstract

In this note we prove the following conjecture of Nowakowski and Rall: For arbitrary graphs $G$ and $H$ the upper domination number of the Cartesian product $G \,\square \, H$ is at least the product of their upper domination numbers, in symbols: $\Gamma(G \,\square \, H)\ge \Gamma(G)\Gamma(H).$

Publisher

The Electronic Journal of Combinatorics

Subject

Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics

Cited by 7 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On Independent Domination in Direct Products;Graphs and Combinatorics;2022-12-27

2. Edge Weighting Functions on Semitotal Dominating Sets;Graphs and Combinatorics;2017-02-08

3. Domination-Related Parameters in Rooted Product Graphs;Bulletin of the Malaysian Mathematical Sciences Society;2015-08-06

4. Vizing's conjecture: a survey and recent results;Journal of Graph Theory;2011-02-09

5. On the total {k}-domination number of Cartesian products of graphs;Journal of Combinatorial Optimization;2008-02-13

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