Support Independence in Graphs

Selvam Avadayappan; M. Bhuvaneshwari; Rajeev Gandhi

doi:https://doi.org/10.14445/22315373/IJMTT-V56P507

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 56 | Number 1 | Year 2018 | Article Id. IJMTT-V56P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V56P507

Support Independence in Graphs

Selvam Avadayappan, M. Bhuvaneshwari, Rajeev Gandhi

Citation :

Selvam Avadayappan, M. Bhuvaneshwari, Rajeev Gandhi, "Support Independence in Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 56, no. 1, pp. 50-59, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V56P507

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.

Keywords

Splitting graphs, cosplitting graphs, Support of a vertex, Support independence.

References

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Keywords