Two Laplacians for the resistance distance matrix of a graph
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929226086612992 |
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| author | Parab, Shivani Tushar DSouza, Raisa |
| author_facet | Parab, Shivani Tushar DSouza, Raisa |
| contents | In this paper, we present two new matrices, namely the resistance Laplacian and resistance signless Laplacian matrix of a connected graph. We provide a generalized form of these matrices for different classes of graphs, including the complete graph, complete bipartite graph, and cycle. We investigate the spectral properties of these matrices, analyzing their eigenvalues and eigenvectors. Moreover, we introduce a concept similar to graph energy and define it as the resistance Laplacian energy of a graph and further discuss some bounds for this energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15300 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two Laplacians for the resistance distance matrix of a graph Parab, Shivani Tushar DSouza, Raisa Combinatorics 05C50 In this paper, we present two new matrices, namely the resistance Laplacian and resistance signless Laplacian matrix of a connected graph. We provide a generalized form of these matrices for different classes of graphs, including the complete graph, complete bipartite graph, and cycle. We investigate the spectral properties of these matrices, analyzing their eigenvalues and eigenvectors. Moreover, we introduce a concept similar to graph energy and define it as the resistance Laplacian energy of a graph and further discuss some bounds for this energy. |
| title | Two Laplacians for the resistance distance matrix of a graph |
| topic | Combinatorics 05C50 |
| url | https://arxiv.org/abs/2401.15300 |