Abstract
Given a graph , an -edge-weighting is a map , where is a positive integer. For a vertex of , let denote the sum of edge-weights appearing on the edges incident at under the edge-weighting . An -edge-weighting of is said to be equitable irregular if , for every pair of adjacent vertices and in . A graph is said to be equitable irregular if admits an equitable irregular edge-weighting. If is equitable irregular then the equitable irregular strength of is dened to be the smallest positive integer such that there is a -edge-weighting of , and is denoted by . In this paper we initiate a study of this new non-proper edge weighting of graphs.
Citation
I. Sahul Hamid. S. Ashok Kumar. "Equitable irregular edge-weighting of graphs." SUT J. Math. 46 (1) 79 - 91, January 2010. https://doi.org/10.55937/sut/1280430251
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