Paper Info
Title
Minimum Eccentric Connectivity Index for Graphs with Fixed Order and Fixed Number of Pending Vertices.
Abstract
The eccentric connectivity index of a connected graph $G$ is the sum over all vertices $v$ of the product $d_{G}(v) e_{G}(v)$, where $d_{G}(v)$ is the degree of $v$ in $G$ and $e_{G}(v)$ is the maximum distance between $v$ and any other vertex of $G$. This index is helpful for the prediction of biological activities of diverse nature, a molecule being modeled as a graph where atoms are represented by vertices and chemical bonds by edges. We characterize those graphs which have the smallest eccentric connectivity index among all connected graphs of a given order $n$. Also, given two integers $n$ and $p$ with $pleq n-1$, we characterize those graphs which have the smallest eccentric connectivity index among all connected graphs of order $n$ with $p$ pending vertices.
Year
DOI
Venue
2018
10.2298/yjor181115010d
Yugoslav Journal of Operations Research
Field
DocType
Volume
Integer,Discrete mathematics,Graph,Combinatorics,Vertex (geometry),Connectivity,Mathematics,Topological index
Journal
abs/1809.03158
Citations 
PageRank 
References 
0
0.34
0
Authors
4
Name
Order
Citations
PageRank
Gauvain Devillez100.68
alain hertz21347107.41
Hadrien Melot39514.02
Pierre Hauweele400.68