TY - JOUR

T1 - Integer domination of Cartesian product graphs

AU - Choudhary, K.

AU - Margulies, S.

AU - Hicks, I. V.

N1 - Publisher Copyright:
© Published by Elsevier B.V.

PY - 2015/7/6

Y1 - 2015/7/6

N2 - 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).

AB - 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).

KW - Domination theory

KW - Product graphs

KW - Vizing's conjecture

UR - http://www.scopus.com/inward/record.url?scp=84924257889&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2015.01.032

DO - 10.1016/j.disc.2015.01.032

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AN - SCOPUS:84924257889

SN - 0012-365X

VL - 338

SP - 1239

EP - 1242

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 7

ER -