The Wiener-Type Indices of the Corona of Two Graphs

Hong Bian1, Xiaoling Ma2, Elkin Vumar2, Haizheng Yu2
1School of Mathematical Science, Xinjiang Normal University, Urumai, Xinjiang 830054, P.R.China
2 College of Mathematics and System Sciences Xinjiang University, Urumdi Xinjiang 830046, P.R.China

Abstract

The corona of two graphs \(G\) and \(H\), written as \(G \odot H\), is the graph obtained by taking one copy of \(G\) and \(|V(G)|\) copies of \(H\), and then joining the \(i\)th vertex of \(G\) to every vertex in the \(i\)th copy of \(H\). In this paper, we present the explicit formulae for the Wiener, hyper-Wiener and reverse-Wiener indices of the corona of two graphs.