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 $σ_G(u)$, 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 $S_{1}(G) = \sum_{uv \in E(G)}[σ_G(u)+ σ_G(v)]$ and $S_{2}(G) = \sum_{uv \in E(G)}σ_G(u)σ_G(v)$ 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 $\overline{S_{1}}(G) = \sum_{uv \notin E(G)}[σ_G(u)+ σ_G(v)]$ and $\overline{S_{2}}(G) = \sum_{uv \notin E(G)}σ_G(u)σ_G(v)$ 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.

No reviews yet.

No comments yet.