BibTex RIS Cite

Some Relations Among the Largest Eigenvalues of Product Matrix and Graph Matrices

Year 2015, Volume: 4 Issue: 2, 26 - 34, 08.01.2016

Sezer Sorgun Hatice Topcu Kahraman Birgin Hakan Küçük

https://doi.org/10.17100/nevbiltek.211037

Abstract

We define product matrix as  , where  is an adjacency matrix and  is a diagonal matrix of vertex degrees of a graph . In this paper, some relations among the spectral radius of product matrix and the largest eigenvalues of graph matrices are obtained. We also give numerical results for them.

Keywords

-

References

  • Brualdi R.A., Hoffman A.J., “On the spectral radius of (0,1) matrix”, Linear Algebra Appl., 65, 133-146, 1985.
  • Stanley R.P., “A bound on the spectral radius of graphs with e edges”, Linear Algebra Appl., 67, 267-269, 1987.
  • Hong Y., “A bound on the spectral radius of graphs”, Linear Algebra Appl., 108, 133-140, 1988.
  • Das K.C., “A characterization of graphs which archive the upper bound for the largest Laplacian eigenvalue of graphs”, Linear Algebra Appl., 376, 173-186, 2004.
  • Das K.C., Kumar P. “Bounds on the greatest eigenavlue of graphs”, Indian J. Pure Appl. Math., 34(6), 917-925, 2003.
  • Das K.C., “Proof of conjecture involving the second largest signless Laplacian eigenvalue and the index of graphs”, Linear Algebra Appl., 435, 2420-2424, 2011.
  • Zhang X.-D., “Two sharp upper bounds for the Laplacian eigenvalues”, Linear Algebra Appl., 376, 207-213, 2004.
  • Berman A., Zhang X.-D. “On the spectral radius of graphs with cut vertices”, J. Combin. Thoery Series B, 83, 223-240, 2003.
  • Zhang X.-D., Luo R. “T he spectral radius of triangle-free graphs”, Australas J. Combin., 26, 33-39, 2002.
  • Guo J.-M., “A new upperbound for the Laplacian spectral radius of graphs”, Linear Algebra Appl., 400, 61-66, 2005.
  • Chen Y.,Wang L. “Sharp bounds for the largest eigenvalue of the signless Laplacian of a graph”, Linear Algebra Appl., 433, 908-913, 2010.
  • Lu M., Liu H., Tian F. “An improved upper bound for the Laplacian spectral radius of graphs”, Discrete Math., 309, 6318-6321, 2009.
  • Chen Y., “Properties of spectra of graphs and line graphs”, Appl. Math. J. Ser. B, 3, 371-376, 2002.
  • Feng L., Yu G. “On three conjectures involving of the signless Laplacian spectral radius of graphs”, Pub. De L’Institute Mathematique, 85(99), 35-38, 2009.
  • Cvetkovic D., Rowlinson P., Simic S.K., “Eigenvalue bounds for the signless Laplacian ”, Publ. Inst. Math. (Beograd), 81(95), 11-27, 2007.
  • Aouchiche M., Hansen P., “A survey of automated conjectures in spectral graph theory”, Linear Algebra Appl., 432, 2293-2322, 2010.
  • Akbarietal S., “A relation between the Laplacian and signless Laplacian eigenvalues of a graph”, J. Algebra Combin., 32, 459-464, 2010.
  • Godsil C., Royle G., “Algebraic Graph Theory”, Springer Graduate Texts in Mathematics, Vol. 207, 2002.
  • Horn R.A.., Johnson R., “Matrix Analysis”, Cambridge University Press, New York, 1985.
  • Cvetkovic D., Rowlinson P., Simic S.K., “An Introduction to the Theory of Graph Spectra”, Cambridge University Press, New York, 2010.

Graf Matrisleri ve Çarpım Matrisinin En Büyük Öz Değerleri Arasında Bazı Bağıntılar

Year 2015, Volume: 4 Issue: 2, 26 - 34, 08.01.2016

Sezer Sorgun Hatice Topcu Kahraman Birgin Hakan Küçük

https://doi.org/10.17100/nevbiltek.211037

Abstract

( ) ve ( ) sırasıyla bir grafının komşuluk matrisi ve nokta derecelerinin bir köşegen matrisi olmak üzere ( ) ( ) ( ) matrisini tanımlarız. Bu makalede bu çarpım matrisinin spektral yarıçapı ile graf matrislerinin en büyük öz değerleri arasında bazı bağıntılar elde edilmiştir. Ayrıca nümerik sonuçlar da verilmiştir

Keywords

Graf Matrisleri Laplasyan Komşuluk İşaretsiz Laplasyan Spektral yarıçap

References

  • Brualdi R.A., Hoffman A.J., “On the spectral radius of (0,1) matrix”, Linear Algebra Appl., 65, 133-146, 1985.
  • Stanley R.P., “A bound on the spectral radius of graphs with e edges”, Linear Algebra Appl., 67, 267-269, 1987.
  • Hong Y., “A bound on the spectral radius of graphs”, Linear Algebra Appl., 108, 133-140, 1988.
  • Das K.C., “A characterization of graphs which archive the upper bound for the largest Laplacian eigenvalue of graphs”, Linear Algebra Appl., 376, 173-186, 2004.
  • Das K.C., Kumar P. “Bounds on the greatest eigenavlue of graphs”, Indian J. Pure Appl. Math., 34(6), 917-925, 2003.
  • Das K.C., “Proof of conjecture involving the second largest signless Laplacian eigenvalue and the index of graphs”, Linear Algebra Appl., 435, 2420-2424, 2011.
  • Zhang X.-D., “Two sharp upper bounds for the Laplacian eigenvalues”, Linear Algebra Appl., 376, 207-213, 2004.
  • Berman A., Zhang X.-D. “On the spectral radius of graphs with cut vertices”, J. Combin. Thoery Series B, 83, 223-240, 2003.
  • Zhang X.-D., Luo R. “T he spectral radius of triangle-free graphs”, Australas J. Combin., 26, 33-39, 2002.
  • Guo J.-M., “A new upperbound for the Laplacian spectral radius of graphs”, Linear Algebra Appl., 400, 61-66, 2005.
  • Chen Y.,Wang L. “Sharp bounds for the largest eigenvalue of the signless Laplacian of a graph”, Linear Algebra Appl., 433, 908-913, 2010.
  • Lu M., Liu H., Tian F. “An improved upper bound for the Laplacian spectral radius of graphs”, Discrete Math., 309, 6318-6321, 2009.
  • Chen Y., “Properties of spectra of graphs and line graphs”, Appl. Math. J. Ser. B, 3, 371-376, 2002.
  • Feng L., Yu G. “On three conjectures involving of the signless Laplacian spectral radius of graphs”, Pub. De L’Institute Mathematique, 85(99), 35-38, 2009.
  • Cvetkovic D., Rowlinson P., Simic S.K., “Eigenvalue bounds for the signless Laplacian ”, Publ. Inst. Math. (Beograd), 81(95), 11-27, 2007.
  • Aouchiche M., Hansen P., “A survey of automated conjectures in spectral graph theory”, Linear Algebra Appl., 432, 2293-2322, 2010.
  • Akbarietal S., “A relation between the Laplacian and signless Laplacian eigenvalues of a graph”, J. Algebra Combin., 32, 459-464, 2010.
  • Godsil C., Royle G., “Algebraic Graph Theory”, Springer Graduate Texts in Mathematics, Vol. 207, 2002.
  • Horn R.A.., Johnson R., “Matrix Analysis”, Cambridge University Press, New York, 1985.
  • Cvetkovic D., Rowlinson P., Simic S.K., “An Introduction to the Theory of Graph Spectra”, Cambridge University Press, New York, 2010.
There are 20 citations in total.

Details

Primary Language English
Journal Section Matematik
Authors

Sezer Sorgun

Hatice Topcu

Kahraman Birgin This is me

Hakan Küçük This is me

Publication Date January 8, 2016
Published in Issue Year 2015 Volume: 4 Issue: 2

Cite

APA Sorgun, S., Topcu, H., Birgin, K., Küçük, H. (2016). Some Relations Among the Largest Eigenvalues of Product Matrix and Graph Matrices. Nevşehir Bilim Ve Teknoloji Dergisi, 4(2), 26-34. https://doi.org/10.17100/nevbiltek.211037
AMA Sorgun S, Topcu H, Birgin K, Küçük H. Some Relations Among the Largest Eigenvalues of Product Matrix and Graph Matrices. Nevşehir Bilim ve Teknoloji Dergisi. January 2016;4(2):26-34. doi:10.17100/nevbiltek.211037
Chicago Sorgun, Sezer, Hatice Topcu, Kahraman Birgin, and Hakan Küçük. “Some Relations Among the Largest Eigenvalues of Product Matrix and Graph Matrices”. Nevşehir Bilim Ve Teknoloji Dergisi 4, no. 2 (January 2016): 26-34. https://doi.org/10.17100/nevbiltek.211037.
EndNote Sorgun S, Topcu H, Birgin K, Küçük H (January 1, 2016) Some Relations Among the Largest Eigenvalues of Product Matrix and Graph Matrices. Nevşehir Bilim ve Teknoloji Dergisi 4 2 26–34.
IEEE S. Sorgun, H. Topcu, K. Birgin, and H. Küçük, “Some Relations Among the Largest Eigenvalues of Product Matrix and Graph Matrices”, Nevşehir Bilim ve Teknoloji Dergisi, vol. 4, no. 2, pp. 26–34, 2016, doi: 10.17100/nevbiltek.211037.
ISNAD Sorgun, Sezer et al. “Some Relations Among the Largest Eigenvalues of Product Matrix and Graph Matrices”. Nevşehir Bilim ve Teknoloji Dergisi 4/2 (January 2016), 26-34. https://doi.org/10.17100/nevbiltek.211037.
JAMA Sorgun S, Topcu H, Birgin K, Küçük H. Some Relations Among the Largest Eigenvalues of Product Matrix and Graph Matrices. Nevşehir Bilim ve Teknoloji Dergisi. 2016;4:26–34.
MLA Sorgun, Sezer et al. “Some Relations Among the Largest Eigenvalues of Product Matrix and Graph Matrices”. Nevşehir Bilim Ve Teknoloji Dergisi, vol. 4, no. 2, 2016, pp. 26-34, doi:10.17100/nevbiltek.211037.
Vancouver Sorgun S, Topcu H, Birgin K, Küçük H. Some Relations Among the Largest Eigenvalues of Product Matrix and Graph Matrices. Nevşehir Bilim ve Teknoloji Dergisi. 2016;4(2):26-34.
 Download Cover Image

Dergimizin tarandığı indeksler


12300          20980     2097822081