Status connectivity indices and co-indices of graphs and its computation   to intersection graph, hypercube, Kneser graph and achiral polyhex nanotorus
  The status of a vertex $u$ in a connected graph $G$, denoted by $\sigma_G(u)$, is defined as the sum of the distances between $u$ and all other vertices of a graph $G$. The first and second status connectivity indices of a graph $G$ are defined as $S_{1}(G) = \sum_{uv \in E(G)}[\sigma_G(u)+ \sigma_G(v)]$ and $S_{2}(G) = \sum_{uv \in E(G)}\sigma_G(u)\sigma_G(v)$ respectively, where $E(G)$ denotes the edge set of $G$. In this paper we have defined the first and second status co-indices of a graph $G$ as $\overline{S_{1}}(G) = \sum_{uv \notin E(G)}[\sigma_G(u)+ \sigma_G(v)]$ and $\overline{S_{2}}(G) = \sum_{uv \notin E(G)}\sigma_G(u)\sigma_G(v)$ respectively. Relations between status connectivity indices and status coindices are established. Also these indices are computed for intersection graph, hypercube, Kneser graph and achiral polyhex nanotorus. 
Harishchandra S. Ramane, Ashwini S. Yalnaik, Reza Sharafdini
math.CO math.GR