Paper Info
Title
Extremal graphs of given parameters with respect to the eccentricity distance sum and the eccentric connectivity index
Abstract
Given a connected graph G=(VG,EG), the eccentricity distance sum (EDS) of G is defined as ξd(G)=∑{u,v}⊆VG(ε(u)+ε(v))dG(u,v) and the eccentric connectivity index (ECI) of G is defined as ξc(G)=∑v∈VGε(v)dG(v), where ε(v),dG(v) and dG(u,v) are the eccentricity of v, the degree of v and the distance between u and v in G, respectively. In this paper, some extremal problems on the EDS and the ECI of graphs with given parameters are considered. Firstly, ordering the n-vertex graphs of diameter 2 with respect to the EDS (resp. the ECI) is established. Secondly, the sharp lower bound on the EDS of graphs with given minimum degree is determined. Moreover, the sharp upper bound on the ECI of graphs of diameter 2 with given minimum degree and the sharp lower bound on the ECI of cacti with given radius are established, respectively. Finally sharp upper and lower bounds on the difference between EDS and ECI among all n-vertex graphs of diameter 2 are determined. Thereafter the sharp lower bound on the difference between EDS and ECI among all n-vertex graphs of diameter 2 with given minimum degree (resp. connectivity, edge-connectivity and independence number) is determined.
Year
DOI
Venue
2019
10.1016/j.dam.2018.07.013
Discrete Applied Mathematics
Keywords
Field
DocType
Eccentric connectivity index,Eccentricity distance sum,Diameter,Minimum degree,Independence number
Discrete mathematics,Graph,Combinatorics,Independence number,Vertex (geometry),Eccentricity (behavior),Upper and lower bounds,Connectivity,Topological index,Mathematics
Journal
Volume
ISSN
Citations 
254
0166-218X
2
PageRank 
References 
Authors
0.39
14
3
Name
Order
Citations
PageRank
huihui zhang1307.61
Shuchao Li218335.15
Baogen Xu312219.54