Rainbow edge domination numbers in graphs

H. Abdollahzadeh Ahangar | H. Jahani | N. Jafari Rad

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URL :   http://research.shahed.ac.ir/WSR/WebPages/Report/PaperView.aspx?PaperID=85640
Date :  2018/08/23
Publish in :    Asian-European Journal of Mathematics
DOI :  https://doi.org/10.1142/s1793557120500047
Link :  DOI: 10.1142/S1793557120500047
Keywords :Rainbow, numbers, graphs

Abstract :

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A 2-rainbow edge dominating function (2REDF) of a graph G is a function f from the edge set E(G) to the set of all subsets of the set 1, 2 such that for any edge e ∈ E(G) with f(e) = ∅ the condition Se
∈N(e) f(e) = 1, 2 is fulfilled, where N(e) is the open neighborhood of e. The weight of a 2REDF f is the value Pe∈E(G) f(e). The minimum weight of a 2REDF is the 2-rainbow edge domination number of G, denoted by γ 2r(G). In this paper, we initiate the study of 2-rainbow edge domination in graphs. We present various sharp bounds, exact values and characterizations for the 2-rainbow edge domination number of a graph.