Signless Laplacian spectral characterization of graphs with isolated vertices

Abstract

A graph is said to be DQS if there is no other non-isomorphic graph with the same signless Laplacian spectrum. For a DQS graph G, we show that G ? rK1 is DQS under certain conditions. Applying these results, some DQS graphs with isolated vertices are obtained.

Graphs determined by signless Laplacian spectra

“…✷ In [18], Cámara and Haemers proved that a graph obtained from K n by deleting a matching is DAS. In [36], it have been shown that this graph is also DQS. Remark 5 Some 3-regular DAS graphs are given in [31,43].…”

Signless Laplacian spectral characterization of some graphs

“…The graph G p,n,q is determined by its Laplacian spectrum. Lemma 2.9 ( [20]). Let T be a DLS tree of order n. Then T ∪ rK 1 is DLS.…”

“…In fact, only few graphs with special structures have been proved to be determined by their spectra. For some recent papers on this topic, see [8,18,20,24,30]. As usual, P n , C n , S n and K n stand for the path, the cycle, the star graph and the complete graph of order n, respectively.…”

“…Recently, (signless) Laplacian spectral characterization of disjoint union of graphs have been studied and also the problem of characterizing join graphs which are determined by their (signless) Laplacian spectra is considered. In [20,26,29,35], (signless) Laplacian characterization of graphs with isolated vertices were studied. In [1], Abdian et al investigated signless Laplacian spectral characterization of graphs with independent egdes and isolated vertices.…”

Signless Laplacian determinations of some graphs with independent edges

“…For example, the path, the complement of a path, the complete graph, and the cycle were proved to be determined by their adjacency spectra [6,9]. The path, the complete graph, the cycle, the star and some quasi-star graphs, together with their complement graphs were shown to be determined by their Laplacian spectra [6,9,15,21]. Let K m n be the graph obtained by attaching m pendant vertices to a vertex of the complete graph K n−m , and U n,p be the graph obtained by attaching n − p pendant vertices to a vertex of C p .…”