A NOTE ON THE WEIGHTED WIENER INDEX AND THE WEIGHTED QUASI WIENER INDEX
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
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).
Details
Primary Language
English
Subjects
-
Journal Section
Research Article
Authors
Şerife Büyükköse
GAZI UNIV
Türkiye
Nurşah Mutlu
GAZI UNIV
Türkiye
Gülistan Kaya Gök
HAKKARİ ÜNİVERSİTESİ
Türkiye
Publication Date
December 11, 2017
Submission Date
February 13, 2017
Acceptance Date
October 25, 2017
Published in Issue
Year 2017 Volume: 30 Number: 4