Mansour, Toufik; Schork, Matthias The PI index of bridge and chain graphs. (English) Zbl 1199.05094 MATCH Commun. Math. Comput. Chem. 61, No. 3, 723-734 (2009). Let \(uv\) be an edge of the graph \(G\), connecting the vertices \(u\) and \(v\). Denote by \(m_u(uv| G)\) the number of edges of the graph \(G\) that lie closer to vertex \(u\) than to vertex \(v\). Then the PI index of \(G\) is defined as \(\text{PI}(G)=\sum_{uv\in E(G)}[m_u(uv| G)+m_v(uv| G)]\). Expressions for the PI index of some bridge and chain graphs are determined. Reviewer: Ivan Gutman (Kragujevac) Cited in 2 ReviewsCited in 19 Documents MSC: 05C12 Distance in graphs 05C90 Applications of graph theory Keywords:bridge graphs; chain graphs; PI index PDFBibTeX XMLCite \textit{T. Mansour} and \textit{M. Schork}, MATCH Commun. Math. Comput. Chem. 61, No. 3, 723--734 (2009; Zbl 1199.05094)