2025/07/21 by Jiachang Ye, Ye, Jiachang, Zoran Stanić +3 · 1 citation
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2507.15276
openalex publication_date 2025/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 K1 \vee (Cs ∪ qK2), where q ≥ 0, s ≥ 3, and the number of vertices is at least 16, is DQS; (2). Every graph of the form K1 \vee (Cs1 ∪ Cs2 ∪ ⋯ ∪ Cst ∪ qK2), where t ≥ 2, q ≥ 0, si ≥ 3, and the number of vertices is at least 52, is DQS. Here, Kn and Cn denote the complete graph and the cycle of order n, respectively, while ∪ and \vee represent the disjoint union and the join of graphs. Moreover, the signless Laplacian spectrum of the graphs under consideration is computed explicitly.