in this paper pi, szeged and revised szeged indices of an infinite family of ipr fullereneswith exactly 60+12n carbon atoms are computed. a gap program is also presented that isuseful for our calculations.

We show that on cactus graphs the Szeged index is bounded above by twice Wiener index. For revised situation reversed if graph class further restricted. Namely, all blocks of a are cycles, then its below Additionally, we these bounds sharp and examine cases equality. Along way, provide formulation as sum over vertices, which proves very helpful, may be interesting in other contexts.

In chemical graph theory, many graph parameters, or topological indices, were proposed as estimators of molecular structural properties. Often several variants of an index are considered. The aim is to extend the original concept to larger families of graphs than initially considered, or to make it more precise and discriminant, or yet to make its range of values similar to that of another inde...

The revised edge-Szeged index of a connected graph $G$ is defined as Sze*(G)=∑e=uv∊E(G)( (mu(e|G)+(m0(e|G)/2)(mv(e|G)+(m0(e|G)/2) ), where mu(e|G), mv(e|G) and m0(e|G) are, respectively, the number of edges of G lying closer to vertex u than to vertex v, the number of ed...

The Szeged index of a graph G is defined as S z(G) = ∑ uv = e ∈ E(G) nu(e)nv(e), where nu(e) is number of vertices of G whose distance to the vertex u is less than the distance to the vertex v in G. Similarly, the revised Szeged index of G is defined as S z∗(G) = ∑ uv = e ∈ E(G) ( nu(e) + nG(e) 2 ) ( nv(e) + nG(e) 2 ) , where nG(e) is the number of equidistant vertices of e in G. In this paper,...

Let $G$ be a finite and simple graph with edge set $E(G)$‎. ‎The revised Szeged index is defined as‎ ‎$Sz^{*}(G)=sum_{e=uvin E(G)}(n_u(e|G)+frac{n_{G}(e)}{2})(n_v(e|G)+frac{n_{G}(e)}{2}),$‎ ‎where $n_u(e|G)$ denotes the number of vertices in $G$ lying closer to $u$ than to $v$ and‎ ‎$n_{G}(e)$ is the number of‎ ‎equidistant vertices of $e$ in $G$‎. ‎In this paper...