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Year 2015, Volume: 28 Issue: 4, 709 - 714, 16.12.2015

Abstract

References

  • 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).

The Upper Bound For The Largest Signless Laplacian Eigenvalue Of Weighted Graphs

Year 2015, Volume: 28 Issue: 4, 709 - 714, 16.12.2015

Abstract

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.

References

  • 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).
There are 10 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Mathematics
Authors

Şerife Büyükköse

Nurşah Mutlu This is me

Publication Date December 16, 2015
Published in Issue Year 2015 Volume: 28 Issue: 4

Cite

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. December 2015;28(4):709-714.
Chicago Büyükköse, Şerife, and Nurşah Mutlu. “The Upper Bound For The Largest Signless Laplacian Eigenvalue Of Weighted Graphs”. Gazi University Journal of Science 28, no. 4 (December 2015): 709-14.
EndNote Büyükköse Ş, Mutlu N (December 1, 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 and N. Mutlu, “The Upper Bound For The Largest Signless Laplacian Eigenvalue Of Weighted Graphs”, Gazi University Journal of Science, vol. 28, no. 4, pp. 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 (December 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 and Nurşah Mutlu. “The Upper Bound For The Largest Signless Laplacian Eigenvalue Of Weighted Graphs”. Gazi University Journal of Science, vol. 28, no. 4, 2015, pp. 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.