Abstract
A 2-rainbow edge dominating function (2REDF) of a graph [Formula: see text] is a function [Formula: see text] from the edge set [Formula: see text] to the set of all subsets of the set [Formula: see text] such that for any edge [Formula: see text] with [Formula: see text] the condition [Formula: see text] is fulfilled, where [Formula: see text] is the open neighborhood of [Formula: see text]. The weight of a 2REDF [Formula: see text] is the value [Formula: see text]. The minimum weight of a 2REDF is the 2-rainbow edge domination number of [Formula: see text], denoted by [Formula: see text]. 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.
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