# On the adjacent eccentric distance sum of graphs

Halina Bielak; Katarzyna Wolska

Annales UMCS, Mathematica (2015)

- Volume: 68, Issue: 2, page 1-10
- ISSN: 2083-7402

## Access Full Article

top## Abstract

top## How to cite

topHalina Bielak, and Katarzyna Wolska. "On the adjacent eccentric distance sum of graphs." Annales UMCS, Mathematica 68.2 (2015): 1-10. <http://eudml.org/doc/270008>.

@article{HalinaBielak2015,

abstract = {In this paper we show bounds for the adjacent eccentric distance sum of graphs in terms of Wiener index, maximum degree and minimum degree. We extend some earlier results of Hua and Yu [Bounds for the Adjacent Eccentric Distance Sum, International Mathematical Forum. Vol. 7 (2O02) no. 26. 1280-1294]. The adjaceni eccentric distance sum index of the graph G is defined as [...] where ε(υ) is the eccentricity of the vertex υ, deg(υ) is the degree of the vertex υ and D(υ) = ∑u∊v(G) d (u,υ)is the sum of all distances from the vertex υ.},

author = {Halina Bielak, Katarzyna Wolska},

journal = {Annales UMCS, Mathematica},

keywords = {Adjacent eccentric distance sum; diameter; distance; eccentricity; graph; Wiener index; adjacent eccentric distance sum},

language = {eng},

number = {2},

pages = {1-10},

title = {On the adjacent eccentric distance sum of graphs},

url = {http://eudml.org/doc/270008},

volume = {68},

year = {2015},

}

TY - JOUR

AU - Halina Bielak

AU - Katarzyna Wolska

TI - On the adjacent eccentric distance sum of graphs

JO - Annales UMCS, Mathematica

PY - 2015

VL - 68

IS - 2

SP - 1

EP - 10

AB - In this paper we show bounds for the adjacent eccentric distance sum of graphs in terms of Wiener index, maximum degree and minimum degree. We extend some earlier results of Hua and Yu [Bounds for the Adjacent Eccentric Distance Sum, International Mathematical Forum. Vol. 7 (2O02) no. 26. 1280-1294]. The adjaceni eccentric distance sum index of the graph G is defined as [...] where ε(υ) is the eccentricity of the vertex υ, deg(υ) is the degree of the vertex υ and D(υ) = ∑u∊v(G) d (u,υ)is the sum of all distances from the vertex υ.

LA - eng

KW - Adjacent eccentric distance sum; diameter; distance; eccentricity; graph; Wiener index; adjacent eccentric distance sum

UR - http://eudml.org/doc/270008

ER -

## References

top- [1] Bondy, J. A., Murty, U. S. R., Graph Theory with Applications, Macmillan London and Elsevier, New York, 1976. Zbl1226.05083
- [2] Gupta, S., Singh, M., Madan, A. K., Application of graph theory: Relations of eccentric connectivity index and Wiener’s index with anti-inflammatory activity, J. Math. Anal. Appl. 266 (2002), 259-268. Zbl0987.92021
- [3] 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. Zbl1005.92011
- [4] Hua, H., Yu, G., Bounds for the Adjacent Eccentric Distance Sum, Int. Math. Forum, 7, no. 26 (2002), 1289-1294. Zbl1253.05064
- [5] Ilić, A., Eccentic connectivity index, Gutman, I., Furtula, B., (Eds.) Novel Molecular Structure Descriptors - Theory and Applications II, Math. Chem. Monogr., vol. 9, University of Kragujevac, 2010.
- [6] Ilić, A., Yu, G., Feng, L., On eccentric distance sum of graphs, J. Math. Anal. Appl. 381 (2011), 590-600. Zbl1277.05052
- [7] Sardana, S., Madan, A. K., Predicting anti-HIV activity of TIBO derivatives: a computational approach using a novel topological descriptor, J. Mol. Model 8 (2000), 258-265.
- [8] Yu, G., Feng, L., Ilić, A., On the eccentric distance sum of trees and unicyclic graphs, J. Math. Anal. Appl. 375 (2011), 99-107. [WoS] Zbl1282.05077

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.