In this paper PI, Szeged and revised Szeged indices of an infinite family of IPR fullerenes with exactly 60+12n carbon atoms are computed. A GAP program is also presented that is useful for our calculations.

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...

Let G be a connected graph, nu(e) is the number of vertices of G lying closer to u and nv(e) is the number of vertices of G lying closer to v. Then the Szeged index of G is defined as the sum of nu(e)nv(e), over edges of G.. The PI index of G is a Szeged-like topological index defined as the sum of [mu(e)+ mv(e)], where mu(e) is the number of edges of G lying closer to u than to v, mv(e) is the...

The vertex version of PI index is a molecular structure descriptor which is similar to vertex version of Szeged index. In this paper, we compute the vertex-PI index of TUC4C8(S), TUC4C8(R) and HAC5C7[r, p].

Let e be an edge of a G connecting the vertices u and v. Define two sets N1 (e | G) and N2(e |G) as N1(e | G)= {xV(G) d(x,u) d(x,v)} and N2(e | G)= {xV(G) d(x,v) d(x,u) }.The number of elements of N1(e | G) and N2(e | G) are denoted by n1(e | G) and n2(e | G) , respectively. The Szeged index of the graph G is defined as Sz(G) ( ) ( ) 1 2 n e G n e G e E    . In this paper we compute th...

We resolve two conjectures of Hri\v{n}\'{a}kov\'{a}, Knor and \v{S}krekovski (2019) concerning the relationship between variable Wiener index Szeged for a connected, non-complete graph, one which would imply other. The strong conjecture is that any such graph there critical exponent in $(0,1]$, below larger above larger. weak always exceeding $1$. They proved bipartite graphs, trees. In this no...