Abstract
The total labeling of a graph G = ( V , E ) is a bijection from the union of the vertex set and the edge set of G to the set { 1 , 2 , … , | V ( G ) | + | E ( G ) | } . The edge-weight of an edge under a total labeling is the sum of the label of the edge and the labels of the end vertices of that edge. The vertex-weight of a vertex under a total labeling is the sum of the label of the vertex and the labels of all the edges incident with that vertex. A total labeling is called edge-magic or vertex-magic when all the edge-weights or all the vertex-weights are the same, respectively. When all the edge-weights or all the vertex-weights are different then a total labeling is called edge-antimagic or vertex-antimagic total, respectively. In this paper we deal with the problem of finding a~total labeling of some classes of graphs that is simultaneously vertex-magic and edge-antimagic or simultaneously vertex-antimagic and edge-magic, respectively. We show several results for stars, paths and cycles.
Published Version
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