DQ-integral and DL-integral generalized wheel graphs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916086861004800 |
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| author | Chai, Yirui Wang, Ligong Zhou, Yuwei |
| author_facet | Chai, Yirui Wang, Ligong Zhou, Yuwei |
| contents | A graph G is said to be M-integral (resp. A-integral, D-integral, DL-integral or DQ-integral) if all eigenvalues of its matrix M (resp. adjacency matrix A(G), distance matrix D(G), distance Laplacian matrix DL(G) or distance signless Laplacian matrix DQ(G)) are integers. Lu et al. [Discrete Math, 346 (2023)] defined the generalized wheel graph GW(a, m, n) as the join of two regular graphs aKm and Cn, and obtained all D-integral generalized wheel graphs. Based on the above research, in this paper, we determine all DL-integral and DQ-integral generalized wheel graphs respectively. As byproducts, we give a sufficient and necessary condition for the join of two regular graphs G1 and G2 to be DL-integral, from which we can get infinitely many new classes of DL-integral graphs according to the large number of research results about the A-integral graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05059 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | DQ-integral and DL-integral generalized wheel graphs Chai, Yirui Wang, Ligong Zhou, Yuwei Combinatorics A graph G is said to be M-integral (resp. A-integral, D-integral, DL-integral or DQ-integral) if all eigenvalues of its matrix M (resp. adjacency matrix A(G), distance matrix D(G), distance Laplacian matrix DL(G) or distance signless Laplacian matrix DQ(G)) are integers. Lu et al. [Discrete Math, 346 (2023)] defined the generalized wheel graph GW(a, m, n) as the join of two regular graphs aKm and Cn, and obtained all D-integral generalized wheel graphs. Based on the above research, in this paper, we determine all DL-integral and DQ-integral generalized wheel graphs respectively. As byproducts, we give a sufficient and necessary condition for the join of two regular graphs G1 and G2 to be DL-integral, from which we can get infinitely many new classes of DL-integral graphs according to the large number of research results about the A-integral graphs. |
| title | DQ-integral and DL-integral generalized wheel graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2401.05059 |