• Kirchoff Index of Graphs and some Graph Operations

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/124/03/0281-0289

• # Keywords

Kirchhoff index; resistance distance.

• # Abstract

Let 𝑇 be a rooted tree, 𝐺 a connected graph, $x,y\in V(G)$ be fixed and $G_i$’s be $|V(T)|$ disjoint copies of 𝐺 with $x_i$ and $y_i$ denoting the corresponding copies of 𝑥 and 𝑦 in $G_i$, respectively. We define the 𝑇-repetition of 𝐺 to be the graph obtained by joining $y_i$ to $x_j$ for each $i\in V(T)$ and each child 𝑗 of 𝑖. In this paper, we compute the Kirchhoff index of the 𝑇-repetition of 𝐺 in terms of parameters of 𝑇 and 𝐺. Also we study how $Kf(G)$ behaves under some graph operations such as joining vertices or subdividing edges.

• # Author Affiliations

1. Department of Mathematics, College of Sciences, Shiraz University, 71457-44776 Shiraz, Iran

• # Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019