DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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

STRONGLY MULTIPLICATIVE GRAPHS

L.W. Beineke

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

e-mail: beineke@ipfw.edu

S.M. Hegde

Karnataka Regional Engineering College
Srinivasnagar, Karnataka - 574157, India

e-mail: smhegde@krec.ernet.in

Abstract

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.

References

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Received 9 August 2000