Nullity of b-Bridge Coalescence Graphs - Sharaf, Khidir R.; Ibrahim, Nechirvan B. (Sulaimani Journal for Pure and Applied Sciences, 2016)
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.
Keywords: Spectra of a Graph; Nullity of a Graph; b Bridge Graphs