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Title: | The main eigenvalues and number of walks in self-complementary graphs |
Authors: | Farrugia, Alexander Sciriha, Irene |
Keywords: | Eigenvalues Polynomials Mathematics -- Charts, diagrams, etc. Mathematics -- Problems, exercises, etc. |
Issue Date: | 2014 |
Publisher: | Taylor & Francis |
Citation: | Farrugia, A., & Sciriha, I. (2014). The main eigenvalues and number of walks in self-complementary graphs. Linear and Multilinear Algebra, 62(10). |
Abstract: | The number of walks of an arbitrary length in a graph depends only on its main eigenvalues and the orthogonal projections onto the associated eigenspaces. Given that a graph is known to be self-complementary, it is shown that its main eigenvalues are easily recognizable from the spectrum alone. Various results on self-complementary graphs (sc-graphs) are derived. An upper bound for the number (less than ) of main eigenvalues of -vertex sc-graphs is established. An explicit formula for the number of walks of length less than in sc-graphs is also presented. We conclude by showing that, for a self-complementary graph, some or all of the coefficients of the main characteristic polynomial suffice to yield the number of walks of any length. |
URI: | https://www.um.edu.mt/library/oar//handle/123456789/28354 |
Appears in Collections: | Scholarly Works - FacSciMat Scholarly Works - JCMath |
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The_main_eigenvalues_and_number_of_walks_in_self-complementary_graphs_2013.pdf Restricted Access | 231.92 kB | Adobe PDF | View/Open Request a copy |
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