A NOTE ON THE WEIGHTED WIENER INDEX AND THE WEIGHTED QUASI WIENER INDEX

Şerife Büyükköse; Nurşah Mutlu; Gülistan Kaya Gök

Research Article

A NOTE ON THE WEIGHTED WIENER INDEX AND THE WEIGHTED QUASI WIENER INDEX

Year 2017, Volume: 30 Issue: 4, 413 - 419, 11.12.2017

Şerife Büyükköse , Nurşah Mutlu , Gülistan Kaya Gök

Abstract

In
this study, we consider the weighted Wiener index and the weighted Quasi Wiener
index of simple connected weighted graphs and we find some bounds for the
weighted Wiener index and the weighted Quasi Wiener index of the weighted
graphs. Moreover, we obtain some results by using these bounds for weighted and
unweighted graphs.

Keywords

Weighted graph, weighted Wiener index, weighted Quasi Wiener index

References

1. Anderson, W.N. and Morley, T.D., “Eigenvalues of The Laplacian of A Graph”, Linear and Multilinear Algebra, 18(2): 141-145, (1985).
2. Boumal, N. and Cheng, X., “Concentration of the Kirchhoff Index for Erdős-Rényi Graphs”, Systems & Control Letters, 74: 74-80, (2014).
3. Cui, Z. and Liu, B., “On Harary Matrix, Harary Index and Harary Energy”, MATCH Commun. Math. Comput. Chem. 68: 815-823, (2012).
4. Dankelmann, P., Gutman, I., Mukwembi, S., Swart, H.C., “The edge-Wiener Index of a Graph”, Discrete Mathematics 309: 3452-3457 (2009).
5. Fath-Tabar, G.H., Ashrafi, A.R., “New Upper Bounds for Estrada Index of Bipartite Graphs”, Linear Algebra and its Applications 435: 2607-2611, (2011).
6. Horn, R.A. and Johnson, C.R., “Matrix Analysis”, 2 nd ed., Cambridge/United Kingdom:Cambridge University Press, 225-260, 391-425, (2012).
7. Klavzar, S., Nadjafi-Arani, M.J., “Improved Bounds on The Difference Between The Szeged Index and The Wiener Index of Graphs”, European Journal of Combinatorics 39: 148-156, (2014).
8. Morgan, M.J., Mukwembi, S., Swart, H.C., “A Lower Bound on The Eccentric Connectivity Index of a Graph”, Discrete Applied Mathematics 160: 248-258, (2012).
9. Zhang, F., “Matrix Theory: Basic Results And Techniques”, 1 nd ed., New York/USA:Springer-Verlag, 159-173, (1999).
10. Zhou, B., Gutman, I., “Relations Between Wiener, Hyper-Wiener and Zagreb Indices”, Chemical Physics Letters 394: 93-95, (2004).

Year 2017, Volume: 30 Issue: 4, 413 - 419, 11.12.2017

Şerife Büyükköse , Nurşah Mutlu , Gülistan Kaya Gök

Abstract

References

1. Anderson, W.N. and Morley, T.D., “Eigenvalues of The Laplacian of A Graph”, Linear and Multilinear Algebra, 18(2): 141-145, (1985).
2. Boumal, N. and Cheng, X., “Concentration of the Kirchhoff Index for Erdős-Rényi Graphs”, Systems & Control Letters, 74: 74-80, (2014).
3. Cui, Z. and Liu, B., “On Harary Matrix, Harary Index and Harary Energy”, MATCH Commun. Math. Comput. Chem. 68: 815-823, (2012).
4. Dankelmann, P., Gutman, I., Mukwembi, S., Swart, H.C., “The edge-Wiener Index of a Graph”, Discrete Mathematics 309: 3452-3457 (2009).
5. Fath-Tabar, G.H., Ashrafi, A.R., “New Upper Bounds for Estrada Index of Bipartite Graphs”, Linear Algebra and its Applications 435: 2607-2611, (2011).
6. Horn, R.A. and Johnson, C.R., “Matrix Analysis”, 2 nd ed., Cambridge/United Kingdom:Cambridge University Press, 225-260, 391-425, (2012).
7. Klavzar, S., Nadjafi-Arani, M.J., “Improved Bounds on The Difference Between The Szeged Index and The Wiener Index of Graphs”, European Journal of Combinatorics 39: 148-156, (2014).
8. Morgan, M.J., Mukwembi, S., Swart, H.C., “A Lower Bound on The Eccentric Connectivity Index of a Graph”, Discrete Applied Mathematics 160: 248-258, (2012).
9. Zhang, F., “Matrix Theory: Basic Results And Techniques”, 1 nd ed., New York/USA:Springer-Verlag, 159-173, (1999).
10. Zhou, B., Gutman, I., “Relations Between Wiener, Hyper-Wiener and Zagreb Indices”, Chemical Physics Letters 394: 93-95, (2004).

There are 10 citations in total.

Details

Journal Section	Mathematics
Authors	Şerife Büyükköse Nurşah Mutlu Gülistan Kaya Gök
Publication Date	December 11, 2017
Published in Issue	Year 2017 Volume: 30 Issue: 4

Cite

APA	Büyükköse, Ş., Mutlu, N., & Kaya Gök, G. (2017). A NOTE ON THE WEIGHTED WIENER INDEX AND THE WEIGHTED QUASI WIENER INDEX. Gazi University Journal of Science, 30(4), 413-419.
AMA	Büyükköse Ş, Mutlu N, Kaya Gök G. A NOTE ON THE WEIGHTED WIENER INDEX AND THE WEIGHTED QUASI WIENER INDEX. Gazi University Journal of Science. December 2017;30(4):413-419.
Chicago	Büyükköse, Şerife, Nurşah Mutlu, and Gülistan Kaya Gök. “A NOTE ON THE WEIGHTED WIENER INDEX AND THE WEIGHTED QUASI WIENER INDEX”. Gazi University Journal of Science 30, no. 4 (December 2017): 413-19.
EndNote	Büyükköse Ş, Mutlu N, Kaya Gök G (December 1, 2017) A NOTE ON THE WEIGHTED WIENER INDEX AND THE WEIGHTED QUASI WIENER INDEX. Gazi University Journal of Science 30 4 413–419.
IEEE	Ş. Büyükköse, N. Mutlu, and G. Kaya Gök, “A NOTE ON THE WEIGHTED WIENER INDEX AND THE WEIGHTED QUASI WIENER INDEX”, Gazi University Journal of Science, vol. 30, no. 4, pp. 413–419, 2017.
ISNAD	Büyükköse, Şerife et al. “A NOTE ON THE WEIGHTED WIENER INDEX AND THE WEIGHTED QUASI WIENER INDEX”. Gazi University Journal of Science 30/4 (December 2017), 413-419.
JAMA	Büyükköse Ş, Mutlu N, Kaya Gök G. A NOTE ON THE WEIGHTED WIENER INDEX AND THE WEIGHTED QUASI WIENER INDEX. Gazi University Journal of Science. 2017;30:413–419.
MLA	Büyükköse, Şerife et al. “A NOTE ON THE WEIGHTED WIENER INDEX AND THE WEIGHTED QUASI WIENER INDEX”. Gazi University Journal of Science, vol. 30, no. 4, 2017, pp. 413-9.
Vancouver	Büyükköse Ş, Mutlu N, Kaya Gök G. A NOTE ON THE WEIGHTED WIENER INDEX AND THE WEIGHTED QUASI WIENER INDEX. Gazi University Journal of Science. 2017;30(4):413-9.