Bled'11 - 7th Slovenian International Conference on Graph Theory

19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
Home > Timetable > Contribution details
PDF | XML

Relationship Between Edge Wiener, Edge Szeged and Szeged Indices of Graphs with Appluications in Nanoscience

Presented by Prof. Seyed Ali Reza ASHRAFI GHOMROODI
Type: Oral presentation
Track: Mathematical Chemistry

Content

Suppose $G$ is a graph, $w \in V(G)$ and $e = uv, f = ab \in E(G)$. Define $n_u(e)$ and $m_u(e)$ to be the number of vertices and edges lying closer to $u$ than $v$, respectively. The quantities $n_v(e)$ and $m_v(e)$ are defined analogously. We also define $d(w, e) = min\{ d(w,u), d(w,v)\}$ and $d(e,f) = min\{ d(u,f), d(v,f)\}$. The edge Wiener, edge Szeged and Szeged indices of $G$ are defined as follows: \begin{eqnarray*} W_e(G) &=& \sum_{\{ e,f \} \subseteq E(G)}D(e,f),\\ Sz_e(G) &=& \sum_{e=uv \in E(G)}m_u(e)m_v(e), Sz(G) &=& \sum_{e=uv \in E(G)}n_u(e)n_v(e). \end{eqnarray*} In this talk some new results regarding the relationship between these topological indices are presented. We also apply our results to compute these topological indices for some classes of molecular graphs applicable in nanoscience.

Place

Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

More