Please use this identifier to cite or link to this item:
https://www.um.edu.mt/library/oar/handle/123456789/28167
Title: | Coalescing Fiedler and core vertices |
Authors: | Ali, Didar A. Gauci, John Baptist Sciriha, Irene Sharaf, Khidir R. |
Keywords: | Mathematics -- Charts, diagrams, etc. Mathematics -- Problems, exercises, etc. |
Issue Date: | 2016 |
Publisher: | Institute of Mathematics. Academy of Sciences of the Czech Republic |
Citation: | Ali, D. A., Gauci, J. B., Sciriha, I., & Sharaf, K. R. (2016). Coalescing Fiedler and core vertices. Czechoslovak Mathematical Journal, 66(3), 971-985. |
Abstract: | 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. |
URI: | https://www.um.edu.mt/library/oar//handle/123456789/28167 |
Appears in Collections: | Scholarly Works - FacSciMat |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Coalescing_Fiedler_and_core_vertices_2016.PDF | 198.7 kB | Adobe PDF | View/Open |
Items in OAR@UM are protected by copyright, with all rights reserved, unless otherwise indicated.