On dominating the Cartesian product of a graph and K2 | Zendy

Bert L. Hartnell | Zendy; Douglas F. Rall | Zendy

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On dominating the Cartesian product of a graph and K₂

Author(s) -

Bert L. Hartnell,

Douglas F. Rall

Publication year - 2004

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.1238

Subject(s) - cartesian product , mathematics , combinatorics , graph , product (mathematics) , discrete mathematics , geometry

In this paper we consider the Cartesian product of an arbitrary graph and a complete graph of order two. Although an upper and lower bound for the domination number of this product follow easily from known results, we are interested in the graphs that actually attain these bounds. In each case, we provide an infinite class of graphs to show that the bound is sharp. The graphs that achieve the lower bound are of particular interest given the special nature of their dominating sets and are investigated further.

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