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$Kite_{p+2,p}$ is determined by its Laplacian spectrum | ||
| Transactions on Combinatorics | ||
| دوره 10، شماره 3، آذر 2021، صفحه 165-170 اصل مقاله (221.06 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2021.126646.1798 | ||
| نویسنده | ||
| Hatice Topcu* | ||
| Department of Mathematics, Nev¸ sehir Hacı Bekta¸ s Veli University, P.O.Box 50300, Nev¸ sehir, Turkey | ||
| چکیده | ||
| $Kite_{n,p}$ 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 $n-p\leq2$. | ||
| کلیدواژه‌ها | ||
| Laplacian matrix؛ kite graph؛ determined by spectrum | ||
| مراجع | ||
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[4] H. Topcu, S. Sorgun and W. H. Haemers, On the spectral characterization of pineapple graphs, Linear Algebra Appl., 507 (2016) 267–273. [5] H. Topcu, S. Sorgun and W. H. Haemers, The graphs cospectral with the pineapple graph, Discrete Appl. Math., 269 (2019) 52–59. [6] F. Liu, J. Siemons and W. Wang, New families of graphs determined by their generalized spectrum, Discrete Math., 342 (2019) 1108–1112. [7] L. Mao, S. M. Cioabă and Wei. Wang, Spectral characterization of the complete graph removing a path of small length, Discrete Appl. Math., 257 (2019) 260–268. [8] M. Liu, H. Shan and X. Gu, Spectral characterization of the complete graph removing a path, Discrete Appl. Math., 284 (2020) 499–512. [9] X. Zhang and H. Zhang, Some graphs determined by their spectra, Linear Algebra Appl., 431 (2009) 1443–1454.
[10] S. Sorgun and H. Topcu, On the spectral characterization of kite graphs, J. Algebra Comb. Discrete Struct. Appl., 3 (2016) 81–90. [11] K. C. Das and M. Liu, Kite graphs are determined by their spectra, Applied Math. and Comp., 297 (2017) 74–78.
[12] H. Topcu and S. Sorgun, The kite graph is determined by its adjacency spectrum, Applied Math. and Comp., 330 (2018) 134–142. [13] S. Sorgun and H. Topcu, On the Laplacian eigenvalues of the kite graph, Anadolu Univ. Bilim ve Teknoloji Dergisi B- Teorik Bilimler, 6 (2018) 1–7. [14] A. E. Brouwer and W. H. Haemers, Spectra of graphs, Springer, Amsterdam, 2011.
[15] D. Cvetković, P. Rowlinson and S. Simić, An introduction to the theory of graph spectra, Cambridge University Press, 2010. | ||
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