{"title":"$Kite_{p+2,p}$ is determined by its Laplacian spectrum","authors":"H. Topcu","doi":"10.22108/TOC.2021.126646.1798","DOIUrl":null,"url":null,"abstract":"$Kite_{n,p}$ denotes the kite graph that is obtained by appending complete graph with order $pgeq4$ 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 $ngeq4$, $nneq5$ and is also determined by its distance spectrum when $ngeq4$ [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 $n-pleq2$.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"10 1","pages":"165-170"},"PeriodicalIF":0.6000,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions on Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22108/TOC.2021.126646.1798","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
$Kite_{n,p}$ denotes the kite graph that is obtained by appending complete graph with order $pgeq4$ 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 $ngeq4$, $nneq5$ and is also determined by its distance spectrum when $ngeq4$ [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 $n-pleq2$.
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