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Title: | On the coefficient of λ in the characteristic polynomial of singular graphs |
Authors: | Sciriha, Irene |
Keywords: | Eigenvectors Mathematics -- Charts, diagrams, etc. Mathematics -- Problems, exercises, etc. |
Issue Date: | 1997 |
Publisher: | Department of Computer Science, University of Manitoba |
Citation: | Sciriha, I. (1997). On the coefficient of λ in the characteristic polynomial of singular graphs. Utilitas Mathematica, 52, 97-111. |
Abstract: | A singular graph, with adjacency matrix A and one zero eigenvalue, has a corresponding eigenvector v0 which is related to L, the coefficient of λ of the characteristic polynomial φ(G, λ) = Det(λI-A). In this paper a simple formula is derived expressing L in terms of the norm of v0. Furthermore it is shown that the ratio of the diagonal cofactors, which are the determinants of the adjacency matrices of the vertex-deleted subgraphs of G, can be obtained from a kernel eigenvector. The non-singular vertex-deleted subgraphs of G are characterised. Results are also obtained for singular graphs with more than one zero eigenvalue. |
URI: | https://www.um.edu.mt/library/oar//handle/123456789/28155 |
Appears in Collections: | Scholarly Works - FacSciMat |
Files in This Item:
File | Description | Size | Format | |
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On_the_coefficient_of_λ_in_the_characteristic_polynomial_of_singular_graphs_1997.pdf | 192.75 kB | Adobe PDF | View/Open |
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