2025/03/23 by Ye, Jiachang, Qian, Jianguo, Stanić, Zoran · 2 citations
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2503.18044
A graph is determined by its signless Laplacian spectrum if there is no other non-isomorphic graph sharing the same signless Laplacian spectrum. Let Cl, Pl, Kl and Ks,l-s be the cycle, the path, the complete graph and the complete bipartite graph with l vertices, respectively. We prove that G≅ K1\vee (Cl1∪ Cl2∪⋯ ∪ Clt∪ sK1), with s≥ 0, t≥ 1, n≥ 22, is determined by the signless Laplacian spectrum if and only if either s=0 or s≥ 1 and li≠ 3 holds for all 1≤ i≤ t, where n is the order of G, and ∪ and \vee stand for the disjoint union and the join of two graphs, respectively. Moreover, for s≥ 1 and lt=3, K1\vee (K1,3∪ Cl1∪ Cl2∪⋯ ∪ C_lt-1∪ (s-1)K1) is fixed as a graph sharing the signless Laplacian spectrum with G. This contribution extends some recently published results.