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 -