ROMAN k-DOMINATION IN GRAPHS

Title & Authors
ROMAN k-DOMINATION IN GRAPHS
Kammerling, Karsten; Volkmann, Lutz;

Abstract
Let k be a positive integer, and let G be a simple graph with vertex set V (G). A Roman k-dominating function on G is a function f : V (G) $\small{\rightarrow}$ {0, 1, 2} such that every vertex u for which f(u) = 0 is adjacent to at least k vertices $\small{\upsilon_1,\;\upsilon_2,\;{\ldots},\;\upsilon_k}$ with $\small{f(\upsilon_i)}$ = 2 for i = 1, 2, $\small{\ldot}$, k. The weight of a Roman k-dominating function is the value f(V (G)) = $\small{\sum_{u{\in}v(G)}}$ f(u). The minimum weight of a Roman k-dominating function on a graph G is called the Roman k-domination number $\small{{\gamma}_{kR}}$(G) of G. Note that the Roman 1-domination number $\small{\gamma_{1R}}$(G) is the usual Roman domination number $\small{\gamma_R}$(G). In this paper, we investigate the properties of the Roman k-domination number. Some of our results extend these one given by Cockayne, Dreyer Jr., S. M. Hedetniemi, and S. T. Hedetniemi [2] in 2004 for the Roman domination number.
Keywords
domination;Roman k-domination;Roman domination;kdomination;
Language
English
Cited by
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