MMN-1867
Some variants of the Szeged index under rooted product of graphs
Mahdieh Azari;Abstract
The Szeged index $Sz(G)$ of a connected graph $G$ is defined as the sum of the terms $n_{u}(e|G)n_{v}(e|G)$ over all edges $e=uv$ of $G$, where $n_{u}(e|G)$ is the number of vertices of $G$ lying closer to $u$ than to $v$ and $n_{v}(e|G)$ is the number of vertices of $G$ lying closer to $v$ than to $u$. In this paper, some variants of the Szeged index such as the edge PI index, edge Szeged index, edge-vertex Szeged index, vertex-edge Szeged index, and revised edge Szeged index are studied under rooted product of graphs. Results are applied to compute these graph invariants for some chemical graphs by specializing components in rooted products.
Vol. 17 (2016), No. 2, pp. 761-775
DOI: 10.18514/MMN.2017.1867