Eccentric distance sum index for some classes of connected graphs

Halina Bielak, Katarzyna Broniszewska

Abstract


In this paper we show some properties of the eccentric distance sum index which is defined as follows \(\xi^{d}(G)=\sum_{v \in V(G)}D(v) \varepsilon(v)\). This index is widely used by chemists and biologists in their researches. We present a lower bound of this index for a new class of graphs.

Keywords


Adjacent eccentric distance sum; diameter; distance; eccentricity; radius; Wiener index

Full Text:

PDF

References


Bondy, J. A., Murty, U. S. R., Graph Theory with Application, Macmillan London, and Elsevier, New York, 1976.

Gupta, S., Singh, M., Madan, A. K., Eccentric distance sum: A novel graph invariant for predicting biological and physical properties, J. Math. Anal. Appl. 275 (2002), 386-401.

Hua, H., Zhang, S., Xu, K., Further results on the eccentric distance sum, Discrete App. Math. 160 (2012), 170-180.

Hua, H., Xu, K., Wen, S., A short and unified proof of Yu et al.’s two results on the eccentric distance sum, J. Math. Anal. Appl. 382 (2011), 364-366.

Ilic, A., Yu, G., Feng, L., On the eccentric distance sum of graphs, J. Math. Anal. Appl. 381 (2011), 590-600.

Wiener, H., Structural determination of paraffin boiling points, J. Amer. Chem. Soc. 69 (1947), 17-20.

Yu, G., Feng, L., Ilic, A., On the eccentric distance sum of trees and unicyclic graphs, J. Math. Anal. Appl. 375 (2011), 99-107.




DOI: http://dx.doi.org/10.17951/a.2017.71.2.25
Date of publication: 2017-12-18 20:31:32
Date of submission: 2017-12-16 22:16:38


Statistics


Total abstract view - 954
Downloads (from 2020-06-17) - PDF - 465

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2017 Halina Bielak, Katarzyna Broniszewska