Nullity of b-Bridge Coalescence Graphs

Nullity of b-Bridge Coalescence Graphs

Khidir R. Sharaf & Nechirvan B. Ibrahim

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

Article info

Original: 13 June. 2015

Revised:28 July. 2015

Accepted:30 August.  2015

Published online: 20 March.  2016

Key Words:

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

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.

Ramyar Abdolrahman Taimur Ismail,
Mar 20, 2016, 5:10 AM