$Kite_{p+2,p}$ is determined by its Laplacian spectrum

Document Type : Research Paper

Author

Department of Mathematics, Nev¸ sehir Hacı Bekta¸ s Veli University, P.O.Box 50300, Nev¸ sehir, Turkey

Abstract

$Kite_{n,p}$ denotes the kite graph that is obtained by appending complete graph with order $p\geq4$ to an endpoint of path graph with order $n-p$‎. ‎It is shown that $Kite_{n,p}$ is determined by its adjacency spectrum for all $p$ and $n$ [H‎. ‎Topcu and ‎S‎. ‎Sorgun‎, ‎The kite graph is determined by its adjacency spectrum‎, ‎Applied Math‎. ‎and Comp.‎, ‎330 (2018) 134--142]‎. ‎For $n-p=1$‎, ‎it is proven that $Kite_{n,p}$ is determined by its signless Laplacian spectrum when $n\geq4$‎, ‎$n\neq5$ and is also determined by its distance spectrum when $n\geq4$ [K‎. ‎C‎. ‎Das and ‎M‎. ‎Liu‎, ‎Kite graphs are determined by their spectra‎, ‎Applied Math‎. ‎and Comp.‎, ‎297 (2017) 74--78]‎. ‎In this note‎, ‎we say that $Kite_{n,p}$ is determined by its Laplacian spectrum for $n-p\leq2$‎.

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Volume 10, Issue 3 - Serial Number 3
September 2021
Pages 165-170
  • Receive Date: 25 December 2020
  • Revise Date: 28 January 2021
  • Accept Date: 20 February 2021
  • Published Online: 01 September 2021