Abstract
A vertex magic total labeling is a bijection from the union of the vertex set and edge set to the consecutive integers 1,2,3,....,v+e with the property that for every u in the vertex set, the sum of the label of u and the label of the edges incident with u is equal to k, for some constant k. In this paper, we establish the vertex magic labeling of some classes of graphs and provide some open problems related to it.
Highlights
Introduction and Preliminaries LetG be a ...nite, undirected graph with no loops and multiple edges
A vertex magic total labeling is a bijection from the union of the vertex set and edge set to the consecutive integers 1; 2; 3; ::::; v + e with the property that for every u in the vertex set, the sum of the label of u and the label of the edges incident with u is equal to k, for some constant k
Let G be a graph with vertex set V (G) and edge set E(G)
Summary
Introduction and Preliminaries LetG be a ...nite, undirected graph with no loops and multiple edges. Two vertices v; w in the vertex set of M (G) are adjacent in M (G) if one of the following holds. A magic graph is a graph whose edges are labeled by positive integers, so that the sum over the edges incident with any vertex is the same, independent of the choice of vertex.
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