Paper Info
Title
On the minimal eccentric connectivity indices of bipartite graphs with some given parameters.
Abstract
Let G be a connected graph. The eccentric connectivity index ξc(G) of G is defined as ξc(G)=∑v∈VGdG(v)ϵG(v), where the eccentricity ϵG(v)=maxu∈VGdG(v,u). Zhang et al. (2012) studied the minimal eccentric connectivity indices of graphs. As a continuance of it, in this paper we consider these problems on bipartite graphs. We obtain lower bounds on ξc(G) in terms of the number of edges among n-vertex connected bipartite graphs with given diameter. Among all connected bipartite graphs on n vertices with m edges and diameter at least s, and connected bipartite graphs on n vertices with diameter at least s, we establish the lower bounds on ξc(G), respectively. All the corresponding extremal graphs are identified.
Year
DOI
Venue
2019
10.1016/j.dam.2018.11.011
Discrete Applied Mathematics
Keywords
Field
DocType
Eccentric connectivity index,Eccentricity,Diameter,Distance
Graph,Discrete mathematics,Combinatorics,Vertex (geometry),Eccentricity (behavior),Bipartite graph,Connectivity,Mathematics,Topological index
Journal
Volume
ISSN
Citations 
258
0166-218X
0
PageRank 
References 
Authors
0.34
8
4
Name
Order
Citations
PageRank
Minjie Zhang101.35
Shuchao Li218335.15
Baogen Xu312219.54
Guangfu Wang412.05