Some graphs determined by their signless laplacian (Distance) spectra

Adiga, Chandrashekar and Kinkar Das and Rakshith, B. R. (2020) Some graphs determined by their signless laplacian (Distance) spectra. Electronic Journal of Linear Algebra, 36 (1). pp. 461-472. ISSN 1081-3810

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In literature, there are some results known about spectral determination of graphs with many edges. In [M.~C\'{a}mara and W.H.~Haemers. Spectral characterizations of almost complete graphs. {\em Discrete Appl. Math.}, 176:19--23, 2014.], C\'amara and Haemers studied complete graph with some edges deleted for spectral determination. In fact, they found that if the deleted edges form a matching, a complete graph Km provided m≤n−2, or a complete bipartite graph, then it is determined by its adjacency spectrum. In this paper, the graph Kn∖Kl,m (n>l+m) which is obtained from the complete graph Kn by removing all the edges of a complete bipartite subgraph Kl,m is studied. It is shown that the graph Kn∖K1,m with m≥4 is determined by its signless Laplacian spectrum, and it is proved that the graph Kn∖Kl,m is determined by its distance spectrum. The signless Laplacian spectral determination of the multicone graph Kn−2α∨αK2 was studied by Bu and Zhou in [C.~Bu and J.~Zhou. Signless Laplacian spectral characterization of the cones over some regular graphs. {\em Linear Algebra Appl.}, 436:3634--3641, 2012.] and Xu and He in [L. Xu and C. He. On the signless Laplacian spectral determination of the join of regular graphs. {\em Discrete Math. Algorithm. Appl.}, 6:1450050, 2014.] only for n−2α=1 or 2. Here, this problem is completely solved for all positive integer n−2α. The proposed approach is entirely different from those given by Bu and Zhou, and Xu and He.

Item Type: Article
Additional Information: cited By 0
Subjects: E Mathematical Science > Mathematics
Divisions: Department of > Mathematics
Depositing User: Mr Umendra uom
Date Deposited: 07 May 2021 06:12
Last Modified: 20 Aug 2022 09:39

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