ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 21(1) (2001) 63-75
DOI: 10.7151/dmgt.1133


L.W. Beineke

Indiana University-Purdue University
Fort Wayne, Indiana 46805, USA


S.M. Hegde

Karnataka Regional Engineering College
Srinivasnagar, Karnataka - 574157, India



A graph with p vertices is said to be strongly multiplicative if its vertices can be labelled 1,2,...,p so that the values on the edges, obtained as the product of the labels of their end vertices, are all distinct. In this paper, we study structural properties of strongly multiplicative graphs. We show that all graphs in some classes, including all trees, are strongly multiplicative, and consider the question of the maximum number of edges in a strongly multiplicative graph of a given order.

Keywords: graph labelling, multiplicative labelling.

2000 Mathematics Subject Classification: 05C78.


[1] B.D. Acharya and S.M. Hegde, On certain vertex valuations of a graph, Indian J. Pure Appl. Math. 22 (1991) 553-560.
[2] G.S. Bloom, A chronology of the Ringel-Kotzig conjecture and the continuing quest to call all trees graceful, Ann. N.Y. Acad. Sci. 326 (1979) 32-51, doi: 10.1111/j.1749-6632.1979.tb17766.x.
[3] F.R.K. Chung, Labelings of graphs, Selected Topics in Graph Theory 3 (Academic Press, 1988) 151-168.
[4] P. Erdős, An asymptotic inequality in the theory of numbers, Vestnik Leningrad. Univ. 15 (1960) 41-49.
[5] J.A. Gallian, A dynamic survey of graph labeling, Electronic J. Comb. 5 (1998) #DS6.
[6] R.L. Graham and N.J.A. Sloane, On additive bases and harmonious graphs, SIAM J. Algebraic Discrete Methods 1 (1980) 382-404, doi: 10.1137/0601045.
[7] A. Rosa, On certain valuations of the vertices of a graph, in: Theory of Graphs, Internat. Symposium, Rome, July 1966 (Gordon and Breach, Dunod, 1967) 349-355.

Received 9 August 2000