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

Text
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## Abstract

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 |
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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 |

URI: | http://eprints.uni-mysore.ac.in/id/eprint/15959 |

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