Transactions on Combinatorics (Sep 2021)
$Kite_{p+2,p}$ is determined by its Laplacian spectrum
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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