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Magic Valuations of Finite Graphs

Published online by Cambridge University Press:  20 November 2018

Anton Kotzig  and
Alexander Rosa
Anton Kotzig
Affiliation:
Komenský University, Bratislava, Czechoslovakia University of Calgary, Calgary, Alberta
Alexander Rosa
Affiliation:
Mcmaster University, Hamilton, Ontario
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The purpose of this paper is to investigate for graphs the existence of certain valuations which have some "magic" property. The question about the existence of such valuations arises from the investigation of another kind of valuations which are introduced in [1] and are related to cyclic decompositions of complete graphs into isomorphic subgraphs.

Throughout this paper the word graph will mean a finite undirected graph without loops or multiple edges having at least one edge. By G(m, n) we denote a graph having m vertices and n edges, by V(G) and E(G) the vertex-set and the edge-set of G, respectively. Both vertices and edges are called the elements of the graph.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 4 , December 1970 , pp. 451 - 461
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Rosa, A., On certain valuations of the vertices of a graph, Theory of Graphs, Internat. Sympos., ICC Rome 1966, Paris, Dunod (1967), 349-355.Google Scholar