BibTex RIS Kaynak Göster

The Upper Bound for the Largest Signless Laplacian Eigenvalue of Weighted Graphs

Yıl 2015, Cilt: 28 Sayı: 4, 709 - 714, 17.02.2015

Öz

In this study, we find an upper bound for the largest signless Laplacian eigenvalue of simple connected weighted graphs, where the edge weights are positive definite square matrices. Also we obtain some results on weighted and unweighted graphs by using this bound.

Kaynakça

  • REFERENCES
  • Anderson, W.N. and Morley, T.D., “Eigenvalues Of The Laplacian Of A Graph”, Linear and Multilinear Algebra, 18(2): 141-145, (1985).
  • Das, K.C. and Bapat, R.B., “A Sharp Upper Bound On The Largest Laplacian Eigenvalue Of Weighted Graphs”, Linear Algebra and its Applications, 409: 153-165, (2005).
  • Das, K.C., “Extremal Graph Characterization From The Upper Bound Of The Laplacian Spectral Radius Of Weighted Graphs”, Linear Algebra and its Applications, 427(1): 55-69, (2007).
  • Das, K.C. and Bapat, R.B., “A Sharp Upper Bound On The Spectral Radius Of Weighted Graphs”, Discrete Mathematics, 308(15): 3180-3186, (2008).
  • Horn, R.A. and Johnson, C.R., “Matrix Analysis”, 2 nd ed., Cambridge/United Kingdom:Cambridge University Press, 225-260, 391-425, (2012).
  • Maden, A.D., Das, K.C. and Çevik, A.S., “Sharp Upper Bounds On The Spectral Radius Of The Signless Laplacian Matrix Of A Graph”, Applied Mathematics and Computation, 219(10): 5025-5032, (2013).
  • Sorgun, S. and Büyükköse, Ş., “On The Bounds For The Largest Laplacian Eigenvalues Of Weighted Graphs”, Discrete Optimization, 9(2): 122-129, (2012).
  • Sorgun, S., Büyükköse, Ş. and Özarslan, H.S., “An Upper Bound On The Spectral Radius Of Weighted Graphs”, Hacettepe Journal of Mathematics and Statistics, 42(5): 517-524, (2013).
  • Zhang, F., “Matrix Theory: Basic Results And Techniques”, 1 nd ed., New York/USA:Springer-Verlag, 159-173, (1999).
Yıl 2015, Cilt: 28 Sayı: 4, 709 - 714, 17.02.2015

Öz

Kaynakça

  • REFERENCES
  • Anderson, W.N. and Morley, T.D., “Eigenvalues Of The Laplacian Of A Graph”, Linear and Multilinear Algebra, 18(2): 141-145, (1985).
  • Das, K.C. and Bapat, R.B., “A Sharp Upper Bound On The Largest Laplacian Eigenvalue Of Weighted Graphs”, Linear Algebra and its Applications, 409: 153-165, (2005).
  • Das, K.C., “Extremal Graph Characterization From The Upper Bound Of The Laplacian Spectral Radius Of Weighted Graphs”, Linear Algebra and its Applications, 427(1): 55-69, (2007).
  • Das, K.C. and Bapat, R.B., “A Sharp Upper Bound On The Spectral Radius Of Weighted Graphs”, Discrete Mathematics, 308(15): 3180-3186, (2008).
  • Horn, R.A. and Johnson, C.R., “Matrix Analysis”, 2 nd ed., Cambridge/United Kingdom:Cambridge University Press, 225-260, 391-425, (2012).
  • Maden, A.D., Das, K.C. and Çevik, A.S., “Sharp Upper Bounds On The Spectral Radius Of The Signless Laplacian Matrix Of A Graph”, Applied Mathematics and Computation, 219(10): 5025-5032, (2013).
  • Sorgun, S. and Büyükköse, Ş., “On The Bounds For The Largest Laplacian Eigenvalues Of Weighted Graphs”, Discrete Optimization, 9(2): 122-129, (2012).
  • Sorgun, S., Büyükköse, Ş. and Özarslan, H.S., “An Upper Bound On The Spectral Radius Of Weighted Graphs”, Hacettepe Journal of Mathematics and Statistics, 42(5): 517-524, (2013).
  • Zhang, F., “Matrix Theory: Basic Results And Techniques”, 1 nd ed., New York/USA:Springer-Verlag, 159-173, (1999).
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Mathematics
Yazarlar

Şerife Büyükköse

Nurşah Mutlu

Yayımlanma Tarihi 17 Şubat 2015
Yayımlandığı Sayı Yıl 2015 Cilt: 28 Sayı: 4

Kaynak Göster

APA Büyükköse, Ş., & Mutlu, N. (2015). The Upper Bound for the Largest Signless Laplacian Eigenvalue of Weighted Graphs. Gazi University Journal of Science, 28(4), 709-714.
AMA Büyükköse Ş, Mutlu N. The Upper Bound for the Largest Signless Laplacian Eigenvalue of Weighted Graphs. Gazi University Journal of Science. Aralık 2015;28(4):709-714.
Chicago Büyükköse, Şerife, ve Nurşah Mutlu. “The Upper Bound for the Largest Signless Laplacian Eigenvalue of Weighted Graphs”. Gazi University Journal of Science 28, sy. 4 (Aralık 2015): 709-14.
EndNote Büyükköse Ş, Mutlu N (01 Aralık 2015) The Upper Bound for the Largest Signless Laplacian Eigenvalue of Weighted Graphs. Gazi University Journal of Science 28 4 709–714.
IEEE Ş. Büyükköse ve N. Mutlu, “The Upper Bound for the Largest Signless Laplacian Eigenvalue of Weighted Graphs”, Gazi University Journal of Science, c. 28, sy. 4, ss. 709–714, 2015.
ISNAD Büyükköse, Şerife - Mutlu, Nurşah. “The Upper Bound for the Largest Signless Laplacian Eigenvalue of Weighted Graphs”. Gazi University Journal of Science 28/4 (Aralık 2015), 709-714.
JAMA Büyükköse Ş, Mutlu N. The Upper Bound for the Largest Signless Laplacian Eigenvalue of Weighted Graphs. Gazi University Journal of Science. 2015;28:709–714.
MLA Büyükköse, Şerife ve Nurşah Mutlu. “The Upper Bound for the Largest Signless Laplacian Eigenvalue of Weighted Graphs”. Gazi University Journal of Science, c. 28, sy. 4, 2015, ss. 709-14.
Vancouver Büyükköse Ş, Mutlu N. The Upper Bound for the Largest Signless Laplacian Eigenvalue of Weighted Graphs. Gazi University Journal of Science. 2015;28(4):709-14.