Nullity of b-Bridge Coalescence Graphs

Khidir R. Sharaf and Nechirvan B. Ibrahim

Department of Mathematics, Faculty of Science, University of Zakho, Zakho, Kurdistan Region, Iraq.

DOI: https://doi.org/10.17656/jzs.10461

Abstract

The nullity η(G) (degree of singularity) of a graph G is the algebraic multiplicity of the

number zero in the spectrum of G. If G is a graph containing a vertex of degree one and

H be the subgraph obtained from G, by deleting this vertex together with the vertex

adjacent to it then, η(G) = η(H). In this paper, we proved that nullity of a graph is the

maximum number of independent variables in a high zero-sum weighting for it. The

above procedures are applied to evaluate the nullity of b-bridge coalescence graphs.

They are also applied to determine the nullity of edge introducing between t-tuple

coalescence graphs and nullity of paths introducing between (n, m)-tuples of coalescence

graphs.

Key Words:

Spectra of a Graph, Nullity of a Graph, b- Bridge Graphs.

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