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Totally antimagic total graphs

Abstract:

For a graph G a bijection from the vertex set and the edge set of G to the set {1, 2, . . ., |V(G)| + |E(G)|} is called a total labeling of G. The edge-weight of an edge 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 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-antimagic total (vertexantimagic total) if all edge-weights (vertex-weights) are pairwise distinct. If a labeling is simultaneously edge-antimagic total and vertex-antimagic total it is called a totally antimagic total labeling. A graph that admits totally antimagic total labeling is called a totally antimagic total graph.