Integer domination of Cartesian product graphs

K. Choudhary, S. Margulies*, I. V. Hicks

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Given a graph G, a dominating set D is a set of vertices such that any vertex not in D has at least one neighbor in D. A {k}-dominating multiset Dk is a multiset of vertices such that any vertex in G has at least k vertices from its closed neighborhood in Dk when counted with multiplicity. In this paper, we utilize the approach developed by Clark and Suen (2000) to prove a "Vizing-like" inequality on minimum {k}-dominating multisets of graphs G,H and the Cartesian product graph G□H. Specifically, denoting the size of a minimum {k}-dominating multiset as γ{k}(G), we demonstrate that γ{k}(G)γ{k}(H)≤2kγ{;bsubesub(G□H).

Original languageEnglish
Pages (from-to)1239-1242
Number of pages4
JournalDiscrete Mathematics
Issue number7
StatePublished - 6 Jul 2015
Externally publishedYes


  • Domination theory
  • Product graphs
  • Vizing's conjecture


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