- Title
- Totally antimagic total graphs
- Creator
- Bača, Martin; Miller, Mirka; Phanalasy, Oudone; Ryan, Joe; Semaničová-Feňovčíková, Andrea; Sillasen, Anita Abildgaard
- Relation
- Australasian Journal of Combinatorics Vol. 61, Issue Part 1, p. 42-56
- Relation
- https://ajc.maths.uq.edu.au/?page=get_volumes&volume=61
- Publisher
- Centre for Discrete Mathematics & Computing
- Resource Type
- journal article
- Date
- 2015
- Description
- 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.
- Subject
- antimagic labeling; vertex set; vertices; total graphs
- Identifier
- http://hdl.handle.net/1959.13/1332998
- Identifier
- uon:26991
- Identifier
- ISSN:1034-4942
- Language
- eng
- Full Text
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