Tricyclic and Tetracyclic Graphs with Maximum and Minimum Eccentric Connectivity

Author(s):

M. Tavakoli , F. Rahbarnia , A. R. Ashrafi

Abstract:
Let $G$ be a connected graph on $n$ vertices. $G$ is called tricyclic if it has $n 2$ edges, and tetracyclic if $G$ has exactly $n 3$ edges. Suppose $mathcal{C}_n$ and $mathcal{D}_n$ denote the set of all tricyclic and tetracyclic $n-$vertex graphs, respectively. The aim of this paper is to calculate the minimum and maximum of eccentric connectivity index in $mathcal{C}_n$ and $mathcal{D}_n$.
Keywords:

Tricyclic graph , Tetracyclic graph , Eccentric connectivity index

Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:11 Issue: 1, May 2016
Pages:
137 to 143
https://www.magiran.com/p1527371