Topological indices are one of the oldest and most widely used descriptors in Quantitative StructureProperties Relationvhips (QSPR). Amongst the topological indices used a,s descriptors in QSPIC., the Wienerindex is by far the most popular index. as it has been shown that the Wiener index has a strong correlationwith the chemical propenies of the compound.In this study, the relationship between...

The Wiener index of a network, introduced by the chemist Harry [30], is sum distances between all pairs nodes in network. This index, originally used chemical graph representations non-hydrogen atoms molecule, considered to be fundamental and useful network descriptor. We study problem constructing geometric networks on point sets Euclidean space that minimize index: given set P n points $$\mat...

let $g$ be a non-abelian group and let $z(g)$ be the center of $g$. associate with $g$ there is agraph $gamma_g$ as follows: take $gsetminus z(g)$ as vertices of$gamma_g$ and joint two distinct vertices $x$ and $y$ whenever$yxneq yx$. $gamma_g$ is called the non-commuting graph of $g$. in recent years many interesting works have been done in non-commutative graph of groups. computing the clique...

The sum of distances between all pairs of vertices W (G) in a connected graph G as a graph invariant was first introduced by Wiener [9] in 1947. He observed a correlation between boiling points of paraffins and this invariant, which has later become known as Wiener index of a graph. Today, the Wiener index is one of the most widely used descriptors in chemical graph theory. Due to its strong co...

The Wiener index is one of the oldest graph parameter which is used to study molecular-graph-based structure. This parameter was first proposed by Harold Wiener in 1947 to determining the boiling point of paraffin. The Wiener index of a molecular graph measures the compactness of the underlying molecule. This parameter is wide studied area for molecular chemistry. It is used to study the physio...