Double Domination in the Cartesian and Tensor Products of Graphs

• Journal title : Kyungpook mathematical journal
• Volume 55, Issue 2,  2015, pp.279-287
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2015.55.2.279
Title & Authors
Double Domination in the Cartesian and Tensor Products of Graphs
CUIVILLAS, ARNEL MARINO; CANOY, SERGIO R. JR.;

Abstract
A subset S of V (G), where G is a graph without isolated vertices, is a double dominating set of G if for each $\small{x{{\in}}V(G)}$, $\small{{\mid}N_G[x]{\cap}S{\mid}{\geq}2}$. This paper, shows that any positive integers a, b and n with $\small{2{\leq}a}$<$\small{b}$, $\small{b{\geq}2a}$ and $\small{n{\geq}b+2a-2}$, can be realized as domination number, double domination number and order, respectively. It also characterize the double dominating sets in the Cartesian and tensor products of two graphs and determine sharp bounds for the double domination numbers of these graphs. In particular, it show that if G and H are any connected non-trivial graphs of orders n and m respectively, then $\small{{\gamma}_{{\times}2}(G{\square}H){\leq}min\{m{\gamma}_2(G),n{\gamma}_2(H)\}}$, where $\small{{\gamma}_2}$, is the 2-domination parameter.
Keywords
Domination;double domination;Cartesian;tensor product;
Language
English
Cited by
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