Coalescing Fiedler and core vertices

Czechoslovak Mathematical Journal

Didar A. ¹  John Baptist Gauci¹  Ali² 

[1] Department of Mathematics, Faculty of Science, University of Zakho, 2 Duhok, Iraq;Irene Sciriha (corresponding author), Department of Mathematics, Faculty of Science, University of Malta, Msida MSD 2080, Malta

关键词: nullity;    core vertex;    Fiedler vertex;    cut-vertices;    coalescence;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

The nullity of a graph $G$ is the multiplicity of zero as an eigenvalue in the spectrum of its adjacency matrix. From the interlacing theorem, derived from Cauchy's inequalities for matrices, a vertex of a graph can be a core vertex if, on deleting the vertex, the nullity decreases, or a Fiedler vertex, otherwise. We adopt a graph theoretical approach to determine conditions required for the identification of a pair of prescribed types of root vertices of two graphs to form a cut-vertex of unique type in the coalescence. Moreover, the nullity of subgraphs obtained by perturbations of the coalescence $G$ is determined relative to the nullity of $G$. This has direct applications in spectral graph theory as well as in the construction of certain ipso-connected nano-molecular insulators.

【 授权许可】

Unknown