# Totally antimagic total graphs

Martin Bača, Mirka Miller, Oudone Phanalasy, Joe Ryan, Andrea Semaničová-Feňovčíková, Anita Abildgaard Sillasen

Producción científica: Contribución a una revistaArtículorevisión exhaustiva

11 Citas (Scopus)

## Resumen

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.

In this paper we deal with the problem of finding totally antimagic total labeling of some classes of graphs. We prove that paths, cycles, stars, double-stars and wheels are totally antimagic total. We also show that a union of regular totally antimagic total graphs is a totally antimagic total graph.

Idioma original Inglés 42-56 15 Australasian Journal of Combinatorics 61 1 Publicada - 2015 Sí

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