Öz
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.
Anahtar Kelimeler
Weighted graph weighted Wiener index weighted Quasi Wiener index
Kaynakça
- 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).
Öz
Kaynakça
- 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).
Ayrıntılar
| Bölüm | Mathematics |
|---|---|
| Yazarlar | |
| Yayımlanma Tarihi | 11 Aralık 2017 |
| Yayımlandığı Sayı | Yıl 2017 Cilt: 30 Sayı: 4 |