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On the spectral characterization of kite graphs

Year 2016, , 81 - 90, 15.05.2016
https://doi.org/10.13069/jacodesmath.01767

Abstract

The Kite graph, denoted by $Kite_{p,q}$ is obtained by appending a complete graph $K_{p}$ to a pendant vertex of a path $P_{q}$. In this paper, firstly we show that no two non-isomorphic kite graphs are cospectral w.r.t the adjacency matrix. Let $G$ be a graph which is cospectral with $Kite_{p,q}$ and let $w(G)$ be the clique number of $G$. Then, it is shown that $w(G)\geq p-2q+1$. Also, we prove that $Kite_{p,2}$ graphs are determined by their adjacency spectrum.

References

  • [1] R. Boulet, B. Jouve, The lollipop graph is determined by its spectrum, Electron. J. Combin. 15(1) (2008) Research Paper 74, 43 pp.
  • [2] M. Camara, W. H. Haemers, Spectral characterizations of almost complete graphs, Discrete Appl. Math. 176 (2014) 19–23.
  • [3] M. D. Cvetkovic, P. Rowlinson, S. Simic, An Introduction to the Theory of Graph Spectra, Cambridge University Press, 2010.
  • [4] E.R. van Dam, W. H. Haemers, Which graphs are determined by their spectrum?, Linear Algebra Appl. 373 (2003) 241–272.
  • [5] E.R. van Dam, W. H. Haemers, Developments on spectral characterizations of graphs, Discrete Math. 309(3) (2009) 576–586.
  • [6] M. Doob, W. H. Haemers, The complement of the path is determined by its spectrum, Linear Algebra Appl. 356(1-3) (2002) 57–65.
  • [7] N. Ghareghani, G. R. Omidi, B. Tayfeh-Rezaie, Spectral characterization of graphs with index at most $\sqrt{2+\sqrt{5}}$, Linear Algebra Appl. 420(2-3) (2007) 483–486.
  • [8] W. H. Haemers, X. Liu, Y. Zhang, Spectral characterizations of lollipop graphs, Linear Algebra Appl. 428(11-12) (2008) 2415–2423.
  • [9] F. Liu, Q. Huang, J. Wang, Q. Liu, The spectral characterization of $\infty$-graphs, Linear Algebra Appl. 437(7) (2012) 1482–1502.
  • [10] M. Liu, H. Shan, K. Ch. Das, Some graphs determined by their (signless) Laplacian spectra, Linear Algebra Appl. 449 (2014) 154–165.
  • [11] X. Liu, Y. Zhang, X. Gui, The multi-fan graphs are determined by their Laplacian spectra, Discrete Math. 308(18) (2008) 4267–4271.
  • [12] V. Nikiforov, Some inequalities for the largest eigenvalue of a graph, Combin. Probab. Comput. 11(2) (2002) 179–189.
  • [13] G. R. Omidi, On a signless Laplacian spectral characterization of T-shape trees, Linear Algebra Appl. 431(9) (2009) 1607–1615.
  • [14] D. Stevanovic, P. Hansen, The minimum spectral radius of graphs with a given clique number, Electron. J. Linear Algebra. 17 (2008) 110–117.
  • [15] X. Zhang, H. Zhang, Some graphs determined by their spectra, Linear Algebra Appl. 431(9) (2009) 1443–1454.
Year 2016, , 81 - 90, 15.05.2016
https://doi.org/10.13069/jacodesmath.01767

Abstract

References

  • [1] R. Boulet, B. Jouve, The lollipop graph is determined by its spectrum, Electron. J. Combin. 15(1) (2008) Research Paper 74, 43 pp.
  • [2] M. Camara, W. H. Haemers, Spectral characterizations of almost complete graphs, Discrete Appl. Math. 176 (2014) 19–23.
  • [3] M. D. Cvetkovic, P. Rowlinson, S. Simic, An Introduction to the Theory of Graph Spectra, Cambridge University Press, 2010.
  • [4] E.R. van Dam, W. H. Haemers, Which graphs are determined by their spectrum?, Linear Algebra Appl. 373 (2003) 241–272.
  • [5] E.R. van Dam, W. H. Haemers, Developments on spectral characterizations of graphs, Discrete Math. 309(3) (2009) 576–586.
  • [6] M. Doob, W. H. Haemers, The complement of the path is determined by its spectrum, Linear Algebra Appl. 356(1-3) (2002) 57–65.
  • [7] N. Ghareghani, G. R. Omidi, B. Tayfeh-Rezaie, Spectral characterization of graphs with index at most $\sqrt{2+\sqrt{5}}$, Linear Algebra Appl. 420(2-3) (2007) 483–486.
  • [8] W. H. Haemers, X. Liu, Y. Zhang, Spectral characterizations of lollipop graphs, Linear Algebra Appl. 428(11-12) (2008) 2415–2423.
  • [9] F. Liu, Q. Huang, J. Wang, Q. Liu, The spectral characterization of $\infty$-graphs, Linear Algebra Appl. 437(7) (2012) 1482–1502.
  • [10] M. Liu, H. Shan, K. Ch. Das, Some graphs determined by their (signless) Laplacian spectra, Linear Algebra Appl. 449 (2014) 154–165.
  • [11] X. Liu, Y. Zhang, X. Gui, The multi-fan graphs are determined by their Laplacian spectra, Discrete Math. 308(18) (2008) 4267–4271.
  • [12] V. Nikiforov, Some inequalities for the largest eigenvalue of a graph, Combin. Probab. Comput. 11(2) (2002) 179–189.
  • [13] G. R. Omidi, On a signless Laplacian spectral characterization of T-shape trees, Linear Algebra Appl. 431(9) (2009) 1607–1615.
  • [14] D. Stevanovic, P. Hansen, The minimum spectral radius of graphs with a given clique number, Electron. J. Linear Algebra. 17 (2008) 110–117.
  • [15] X. Zhang, H. Zhang, Some graphs determined by their spectra, Linear Algebra Appl. 431(9) (2009) 1443–1454.
There are 15 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Sezer Sorgun

Hatice Topcu

Publication Date May 15, 2016
Published in Issue Year 2016

Cite

APA Sorgun, S., & Topcu, H. (2016). On the spectral characterization of kite graphs. Journal of Algebra Combinatorics Discrete Structures and Applications, 3(2), 81-90. https://doi.org/10.13069/jacodesmath.01767
AMA Sorgun S, Topcu H. On the spectral characterization of kite graphs. Journal of Algebra Combinatorics Discrete Structures and Applications. May 2016;3(2):81-90. doi:10.13069/jacodesmath.01767
Chicago Sorgun, Sezer, and Hatice Topcu. “On the Spectral Characterization of Kite Graphs”. Journal of Algebra Combinatorics Discrete Structures and Applications 3, no. 2 (May 2016): 81-90. https://doi.org/10.13069/jacodesmath.01767.
EndNote Sorgun S, Topcu H (May 1, 2016) On the spectral characterization of kite graphs. Journal of Algebra Combinatorics Discrete Structures and Applications 3 2 81–90.
IEEE S. Sorgun and H. Topcu, “On the spectral characterization of kite graphs”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 3, no. 2, pp. 81–90, 2016, doi: 10.13069/jacodesmath.01767.
ISNAD Sorgun, Sezer - Topcu, Hatice. “On the Spectral Characterization of Kite Graphs”. Journal of Algebra Combinatorics Discrete Structures and Applications 3/2 (May 2016), 81-90. https://doi.org/10.13069/jacodesmath.01767.
JAMA Sorgun S, Topcu H. On the spectral characterization of kite graphs. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016;3:81–90.
MLA Sorgun, Sezer and Hatice Topcu. “On the Spectral Characterization of Kite Graphs”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 3, no. 2, 2016, pp. 81-90, doi:10.13069/jacodesmath.01767.
Vancouver Sorgun S, Topcu H. On the spectral characterization of kite graphs. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016;3(2):81-90.