Strongly \star-graphs

Chandrashekara Adiga, and Somashekara, D. D. (1999) Strongly \star-graphs. Math. Forum, 13. pp. 31-36.

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Abstract

Review : A graph of order n is said to be a strongly ⋆-graph if its vertices can be assigned the values 1,2,…,n in such a way that, when an edge whose vertices are labeled i and j is labeled with the value i+j+ij, all edges have different labels. This property is a variation on that of strong multiplicity of graphs, as investigated by L. W. Beineke and S. M. Hegde [Discuss. Math. Graph Theory 21 (2001), no. 1, 63–75; MR1867487 (2002g:05161)], the only difference being that there the operation used to label the edges is simple multiplication. In the present note, it is shown that all trees, cycles, and grids are strongly ⋆-graphs (all are also strongly multiplicative). Further, the authors consider the problem of determining the maximum number of edges in any strongly ⋆-graph of given order and relate it to the corresponding problem for strongly multiplicative graphs.

Item Type: Article
Subjects: Physical Sciences > Mathematics
Divisions: PG Campuses > Manasagangotri, Mysore > Mathematics
Depositing User: Kodandarama
Date Deposited: 28 May 2013 02:50
Last Modified: 26 Aug 2013 05:06
URI: http://eprints.uni-mysore.ac.in/id/eprint/10902

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