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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 3 | Issue 1 | Year 2012 | Article Id. IJMTT-V3I1P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V3I1P503

On Strongly Multiplicative Graphs


M. Muthusamy , K.C. Raajasekar , J. Baskar Babujee
Abstract

A graph G with p vertices and q edges is said to be strongly multiplicative if the vertices are assigned distinct numbers 1, 2, 3, …, p such that the labels induced on the edges by the product of the end vertices are distinct. We prove some of the special graphs obtained through graph operations such as Cn + (a graph obtained by adding pendent edge for each vertex of the cycle Cn), (Pn , mK1 ) +N2 , Pn + mK1 and Cn d (cycle Cn with non-intersecting chords) are strongly multiplicative.

Keywords
Graph, labeling, path, cycle, relation, function.
References

[1] B. D. Acharya, K. A. Germina, and V. Ajitha, Multiplicatively indexable graphs, in Labeling of Discrete Structures and Applications, Narosa Publishing House, New Delhi, 2008, 29-40.
[2] C. Adiga, H. N. Ramaswamy, and D. D. Somashekara, A note on strongly multiplicative graphs, Discuss. Math., 24 (2004) 81-83.
[3] J. Baskar Babujee, L. Shobana, “Graph from Relations and its Labeling”, European Journal of Scientific Research ,Vol.64 No.3 (2011), pp. 463-471.
[4] L. W. Beineke and S. M. Hegde, Strongly multiplicative graphs, Discuss. Math. Graph Theory, 21 (2001) 63-75.
[5] Gallian, J.A., “A Dynamic Survey of Graph Labeling”, Electronic Journal of Combinatorics [2010].
[6] K. A. Germina and V. Ajitha, Strongly multiplicative graphs, unpublished.
[7] M. A. Seoud and A. Zid, Strong multiplicativity of unions and corona of paths and complete graphs, Proc. Math. Phys. Soc. Egypt, 74 (1999) 59-71.

Citation :

M. Muthusamy , K.C. Raajasekar , J. Baskar Babujee, "On Strongly Multiplicative Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 3, no. 1, pp. 13-18, 2012. Crossref, https://doi.org/10.14445/22315373/IJMTT-V3I1P503

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