Covering matrices of a graph

S. R. Jayaram; Divya Rashmi S V

doi:https://doi.org/10.14445/22315373/IJMTT-V46P508

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 46 | Number 1 | Year 2017 | Article Id. IJMTT-V46P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V46P508

Covering matrices of a graph

S. R. Jayaram, Divya Rashmi S V

Abstract

Given a Graph G=((V(G), E(G)), and a subset S V(G), S with a given property(covering set, Dominating set, Neighbourhood set), we define a matrix taking a row for each of the minimal set corresponding to the given property and a column for each of the vertex of G. The elements of the matrix are 1 or 0 respectively as the vertex is contained in minimal set or otherwise. That is matrix (mij) has elements mij and mij = 1 if ith row minimal set contains jth vertex = 0 otherwise This paper initiates a study on these new types of matrices of a graph and we characterize such matrices for some special classes of graphs.

Keywords

Covering set, dominating set, neighbourhood number, Point covering number, matrix of a graph.

References

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Citation :

S. R. Jayaram, Divya Rashmi S V, "Covering matrices of a graph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 46, no. 1, pp. 37-42, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V46P508