Abstract

In any graph G, the support of a vertex is defined as the sum of degrees of its neighbours. A graph G is said to be balanced, if every vertex of G has same support. G is called highly unbalanced when no two vertices of G have same support. In this paper, we introduce the concept of support independence in graphs. A subset S of a vertex set is said to be support independent, if no two vertices in S are having same support. The support independence number of G is the cardinality of maximum support independent set in G. We obtain the support independence number of some standard graphs and derived graphs.

References

1. Selvam Avadayappan and M. Bhuvaneshwari, Cosplitting and coregular graphs, International Journal of Mathematics and Soft Computing, Vol.5, No.1,(2015), 57 -64.
2. Selvam Avadayappan, M. Bhuvaneshwari and R. Iswarya, γ-splitting graphs, International Journal for Research in Applied Science & Engineering Technology, Vol. 4, Issue III, March 2016, 670 – 680.
3. Selvam Avadayappan, M. Bhuvaneshwari and Rajeev Gandhi, Distance in splitting graphs, International Journal of Engineering Sciences and Management Research, 2(12), 50 -54, December 2015.
4. Selvam Avadayappan, M.Bhuvaneshwari and B.Vijaya Lakshmi, β- Splitting graphs, International Journal of Scientific Review and Research in Engineering and Technology, Vol. 1(3), Mar. – Apr. 2016, 84 – 101.
5. Selvam Avadayappan, M.Bhuvaneshwari and R. Sinthu, Support neighbourly irregular graphs, International Journal of Scientific Research and Management , Vol. 4, Issue 3, pp. 4009 – 4014, 2016.
6. Selvam Avadayappan and G. Mahadevan, Highly unbalanced graphs, ANJAC Journal of Sciences, 2(1), 23-27, 2003.
7. R.Balakrishnan and K. Ranganathan, A Text Book of graph Theory, Springer-Verlag, New York, Inc(1999).
8. Sampath Kumar.E, Walikar.H.B, On theSplitting graph of a graph,(1980), J.Karnatak Uni. Sci 25: 13.

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