Splice Graphs and Their Topological Indices

Abstract

Let $G_1=(V_1,E_1)$ and $G_2=(V_2,E_2)$ be two graphs with disjoint vertex sets $V_1$ and $V_2$. Let $u_1 \in V_1$ and $u_2 \in V_2$. A splice of $G_1$ and $G_2$ by vertices $u_1$ and $u_2$, $\mathcal{S}(G_1,G_2;u_1,u_2)$, is defined by identifying the vertices $u_1$ and $u_2$ in the union of $G_1$ and $G_2$. In this paper we calculate the Szeged, edge-Szeged, $PI$, vertex-$PI$ and eccentric connectivity indices of splice graphs.