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The PI index of bridge and chain graphs. (English) Zbl 1199.05094

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.

MSC:

05C12 Distance in graphs
05C90 Applications of graph theory
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