Splice Graphs and Their Topological Indices

Reza Sharafdini; Ivan Gutman

paper

Splice Graphs and Their Topological Indices

arXiv:1611.02819

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 $u_{2}$ , $S (G_{1}, G_{2}; u_{1}, u_{2})$ , 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, $P I$ , vertex- $P I$ and eccentric connectivity indices of splice graphs.