Alhevaz, Abdollah, Baghipur, Maryam, Ganie, Hilal A. and Shang, Yilun (2020) The Generalized Distance Spectrum of the Join of Graphs. Symmetry, 12 (1). p. 169. ISSN 2073-8994
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Abstract
Let G be a simple connected graph. In this paper, we study the spectral properties of the generalized distance matrix of graphs, the convex combination of the symmetric distance matrix D(G) and diagonal matrix of the vertex transmissions Tr(G) . We determine the spectrum of the join of two graphs and of the join of a regular graph with another graph, which is the union of two different regular graphs. Moreover, thanks to the symmetry of the matrices involved, we study the generalized distance spectrum of the graphs obtained by generalization of the join graph operation through their eigenvalues of adjacency matrices and some auxiliary matrices.
| Item Type: | Article |
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| Uncontrolled Keywords: | generalized distance matrix (spectrum); distance signless Laplacian matrix; joined union; lexicographic product; complete split graph; graph operation |
| Subjects: | G100 Mathematics |
| Department: | Faculties > Engineering and Environment > Computer and Information Sciences |
| Depositing User: | Elena Carlaw |
| Date Deposited: | 18 Feb 2020 10:47 |
| Last Modified: | 31 Jul 2021 19:48 |
| URI: | http://nrl.northumbria.ac.uk/id/eprint/42111 |
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