Signless Laplacian spectral analysis of a class of graph joins
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909747901366272 |
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| author | Ye, Jiachang Stanić, Zoran Qian, Jianguo |
| author_facet | Ye, Jiachang Stanić, Zoran Qian, Jianguo |
| contents | A graph is said to be determined by its signless Laplacian spectrum (abbreviated as DQS) if no other non-isomorphic graph shares the same signless Laplacian spectrum. In this paper, we establish the following results:
(1). Every graph of the form $K_1 \vee (C_s \cup qK_2)$, where $q \ge 0$, $s \ge 3$, and the number of vertices is at least $16$, is DQS;
(2). Every graph of the form $K_1 \vee (C_{s_1} \cup C_{s_2} \cup \cdots \cup C_{s_t} \cup qK_2)$, where $t \ge 2$, $q \ge 0$, $s_i \ge 3$, and the number of vertices is at least $52$, is DQS.
Here, $K_n$ and $C_n$ denote the complete graph and the cycle of order $n$, respectively, while $\cup$ and $\vee$ represent the disjoint union and the join of graphs. Moreover, the signless Laplacian spectrum of the graphs under consideration is computed explicitly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15276 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Signless Laplacian spectral analysis of a class of graph joins Ye, Jiachang Stanić, Zoran Qian, Jianguo Combinatorics A graph is said to be determined by its signless Laplacian spectrum (abbreviated as DQS) if no other non-isomorphic graph shares the same signless Laplacian spectrum. In this paper, we establish the following results: (1). Every graph of the form $K_1 \vee (C_s \cup qK_2)$, where $q \ge 0$, $s \ge 3$, and the number of vertices is at least $16$, is DQS; (2). Every graph of the form $K_1 \vee (C_{s_1} \cup C_{s_2} \cup \cdots \cup C_{s_t} \cup qK_2)$, where $t \ge 2$, $q \ge 0$, $s_i \ge 3$, and the number of vertices is at least $52$, is DQS. Here, $K_n$ and $C_n$ denote the complete graph and the cycle of order $n$, respectively, while $\cup$ and $\vee$ represent the disjoint union and the join of graphs. Moreover, the signless Laplacian spectrum of the graphs under consideration is computed explicitly. |
| title | Signless Laplacian spectral analysis of a class of graph joins |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2507.15276 |