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https://www.um.edu.mt/library/oar/handle/123456789/28154
Title: | Main eigenvalues and (κ, τ)-regular sets |
Authors: | Cardoso, Domingos M. Sciriha, Irene Zerafa, Cheryl |
Keywords: | Eigenvalues Mathematics -- Charts, diagrams, etc. Mathematics -- Problems, exercises, etc. |
Issue Date: | 2010 |
Publisher: | Elsevier BV |
Citation: | Cardoso, D. M., Sciriha, I., & Zerafa, C. (2010). Main eigenvalues and (κ, τ)-regular sets. Linear Algebra and its Applications, 432(9), 2399-2408. |
Abstract: | A (κ, τ)-regular set is a subset of the vertices of a graph , inducing a κ-regular subgraph such that every vertex not in the subset has τ neighbors in it. A main eigenvalue of the adjacency matrix A of a graph has an eigenvector not orthogonal to the all-one vector j. For graphs with a (κ, τ)-regular set a necessary and sufficient condition for an eigenvalue be non-main is deduced and the main eigenvalues are characterized. These results are applied to the construction of infinite families of bidegreed graphs with two main eigenvalues and the same spectral radius (index) and some relations with strongly regular graphs are obtained. Finally, the determination of (κ, τ)-regular sets is analyzed. |
URI: | https://www.um.edu.mt/library/oar//handle/123456789/28154 |
Appears in Collections: | Scholarly Works - FacSciMat Scholarly Works - JCMath |
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Main_eigenvalues_and_(κ,τ)-regular_sets_2010.pdf Restricted Access | 186.07 kB | Adobe PDF | View/Open Request a copy |
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