User:Mpagey/Padmakar-Ivan Index

{{Userspace draft|source=ArticleWizard|date=March 2010}}

Consider a graph, $G$, such that the edge connecting any two given points, $u$ and $v$, in $G$ is denoted as $e$. Let $n\_\{eu\}(e|G)$ represent the number of edges of $G$ that are closer to point $u$ than point $v$. Similarly, let $n\_\{ev\}(e|G)$ represent the number of edges of $G$ that are closer to $v$ than $u$. In this case, the Padmakar-Ivan Index of the graph $G$, $PI(G)$, is defined as: $PI(G)\; =\; \backslash sum\_\{\backslash forall\{e\}\}\backslash left(\; n\_\{eu\}(e|G)\; +\; n\_\{ev\}(e|G)\; \backslash right)$