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 26(2) (2006) 225-229
DOI: 10.7151/dmgt.1315

AN UPPER BOUND FOR MAXIMUM NUMBER OF EDGES IN A STRONGLY MULTIPLICATIVE GRAPH

Chandrashekar Adiga

Department of Studies in Mathematics
University of Mysore
Manasagangotri, Mysore-570006, India
e-mail: adiga_c@yahoo.com

Mahadev Smitha

Department of Mathematics
Sri Jayachamarajendra College of Engineering
Mysore-570006, India
e-mail: smithamahadev@yahoo.co.in

Abstract

In this note we give an upper bound for λ(n), the maximum number of edges in a strongly multiplicative graph of order n, which is sharper than the upper bounds given by Beineke and Hegde [3] and Adiga, Ramaswamy and Somashekara [2], for n ≥ 28.

Keywords: graph labelling, strongly multiplicative graphs.

2000 Mathematics Subject Classification: 05C78.

References

[1] C. Adiga, H.N. Ramaswamy and D.D. Somashekara, On strongly multiplicative graphs, South East Asian J. Math. & Math. Sc. 2 (2003) 45-47.
[2] C. Adiga, H.N. Ramaswamy and D.D. Somashekara, A note on strongly multiplicative graphs, Discuss. Math. Graph Theory 24 (2004) 81-83, doi: 10.7151/dmgt.1215.
[3] L.W. Beineke and S.M. Hegde, Strongly multiplicative graphs, Discuss. Math. Graph Theory 21 (2001) 63-76, doi: 10.7151/dmgt.1133.
[4] P. Erdős, An asymptotic inequality in the theory of numbers, Vestnik Leningrad. Univ. 15 (1960) 41-49.

Received 18 August 2005
Revised 29 December 2005