Araştırma Makalesi
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ON THE LAPLACIAN EIGENVALUES OF THE KITE GRAPH

Yıl 2018, Cilt: 6 Sayı: 1, 1 - 7, 30.04.2018

Sezer Sorgun Hatice Topcu

https://doi.org/10.20290/aubtdb.315514

Öz

The kite graph is denoted by Kiten,n-p
which is obtained by appending a complete graph Kp to a pendant
vertex of the path graph Pn-p . In this paper, we present some
spectral properties of Laplacian matrix of the kite graph. First we give the
Laplacian characteristic polynomial of Kiten,n-p , then we restrict
its largest Laplacian eigenvalue depending on the clique number. Also we say
that any connected graph which has the same clique number with Kiten,n-p
is isomorphic to the Kiten,n-p under some conditions.

Anahtar Kelimeler

kite graph laplacian eigenvalues

Kaynakça

  • KAYNAKLAR
  • [1] Sorgun S. and Topcu H., On the spectral characterization of kite graphs, J. Algebra Comb. Discrete Struct. Appl. 2016; 3: 81-90.
  • [2] Zhang X. and Zhang H.,Some graphs determined by their spectra, Linear Algebra and its Applications, 2009; 431 (9): 1443–1454.
  • [3] Das K. C. and Liu M., Kite graphs determined by their spectra, Applied Mathematics and Computation, 2017; 297: 74–78.
  • [4] Cvetkovic D., Rowlinson P. and Simic S., An introduction to the theory of graph spectra, Cambridge University Press, 2010.
  • [5] Guo J. M., On the second largest Laplacian eigenvalue of trees, Linear Algebra and its Applications, 2005; 404 : 251–261.
  • [6] Grone R., Merris R., The Laplacian spectrum of graph II, SIAM J. Discrete Math., 1994; 7: 221-229.
  • [7] Godsil C., Royle G.,. Algebraic Graph Theory, Springer, 2001.
  • [8] van Dam, E.R. and Haemers W.H., Which graphs are determined by their spectrum? Linear Algebra and its Applications, 2003; 373: 241–272.

UÇURTMA GRAFIN LAPLASYAN ÖZDEĞERLERİ ÜZERİNE

Yıl 2018, Cilt: 6 Sayı: 1, 1 - 7, 30.04.2018

Sezer Sorgun Hatice Topcu

https://doi.org/10.20290/aubtdb.315514

Öz

p noktalı bir tam grafın, n-p noktalı
bir yol grafın bir dereceli noktasına yeni bir kenar yardımıyla bağlanması ile
elde edilen yeni grafa uçurtma graf denir ve Kiten,n-p ile
gösterilir. Bu çalışmada, uçurtma grafın Laplasyan matrisinin  bazı spektral özellikleri sunulmuştur.
Öncelikle Kiten,n-p grafın Laplasyan karakteristik polinomu elde
edilmiş ve böylece en büyük Laplasyan özdeğer klik sayısına bağlı olarak
sınırlandırılmıştır. Ayrıca bazı özel koşullar altında, Kiten,n-p
grafla aynı klik sayısına sahip herhangi bir bağlantılı grafın Kiten,n-p
grafa izomorf olduğu gösterilmiştir. 

Anahtar Kelimeler

uçurtma graf laplasyan özdeğer

Kaynakça

  • KAYNAKLAR
  • [1] Sorgun S. and Topcu H., On the spectral characterization of kite graphs, J. Algebra Comb. Discrete Struct. Appl. 2016; 3: 81-90.
  • [2] Zhang X. and Zhang H.,Some graphs determined by their spectra, Linear Algebra and its Applications, 2009; 431 (9): 1443–1454.
  • [3] Das K. C. and Liu M., Kite graphs determined by their spectra, Applied Mathematics and Computation, 2017; 297: 74–78.
  • [4] Cvetkovic D., Rowlinson P. and Simic S., An introduction to the theory of graph spectra, Cambridge University Press, 2010.
  • [5] Guo J. M., On the second largest Laplacian eigenvalue of trees, Linear Algebra and its Applications, 2005; 404 : 251–261.
  • [6] Grone R., Merris R., The Laplacian spectrum of graph II, SIAM J. Discrete Math., 1994; 7: 221-229.
  • [7] Godsil C., Royle G.,. Algebraic Graph Theory, Springer, 2001.
  • [8] van Dam, E.R. and Haemers W.H., Which graphs are determined by their spectrum? Linear Algebra and its Applications, 2003; 373: 241–272.
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Bölüm Araştırma Makalesi
Yazarlar

Sezer Sorgun

Hatice Topcu

Yayımlanma Tarihi 30 Nisan 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 6 Sayı: 1

Kaynak Göster

APA Sorgun, S., & Topcu, H. (2018). ON THE LAPLACIAN EIGENVALUES OF THE KITE GRAPH. Anadolu University Journal of Science and Technology B - Theoretical Sciences, 6(1), 1-7. https://doi.org/10.20290/aubtdb.315514
AMA Sorgun S, Topcu H. ON THE LAPLACIAN EIGENVALUES OF THE KITE GRAPH. AUBTD-B. Nisan 2018;6(1):1-7. doi:10.20290/aubtdb.315514
Chicago Sorgun, Sezer, ve Hatice Topcu. “ON THE LAPLACIAN EIGENVALUES OF THE KITE GRAPH”. Anadolu University Journal of Science and Technology B - Theoretical Sciences 6, sy. 1 (Nisan 2018): 1-7. https://doi.org/10.20290/aubtdb.315514.
EndNote Sorgun S, Topcu H (01 Nisan 2018) ON THE LAPLACIAN EIGENVALUES OF THE KITE GRAPH. Anadolu University Journal of Science and Technology B - Theoretical Sciences 6 1 1–7.
IEEE S. Sorgun ve H. Topcu, “ON THE LAPLACIAN EIGENVALUES OF THE KITE GRAPH”, AUBTD-B, c. 6, sy. 1, ss. 1–7, 2018, doi: 10.20290/aubtdb.315514.
ISNAD Sorgun, Sezer - Topcu, Hatice. “ON THE LAPLACIAN EIGENVALUES OF THE KITE GRAPH”. Anadolu University Journal of Science and Technology B - Theoretical Sciences 6/1 (Nisan 2018), 1-7. https://doi.org/10.20290/aubtdb.315514.
JAMA Sorgun S, Topcu H. ON THE LAPLACIAN EIGENVALUES OF THE KITE GRAPH. AUBTD-B. 2018;6:1–7.
MLA Sorgun, Sezer ve Hatice Topcu. “ON THE LAPLACIAN EIGENVALUES OF THE KITE GRAPH”. Anadolu University Journal of Science and Technology B - Theoretical Sciences, c. 6, sy. 1, 2018, ss. 1-7, doi:10.20290/aubtdb.315514.
Vancouver Sorgun S, Topcu H. ON THE LAPLACIAN EIGENVALUES OF THE KITE GRAPH. AUBTD-B. 2018;6(1):1-7.
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