Let $G*H$ be the product $*$ of $G$ and $H$. In this paper we determine the rth power of the graph $G*H$ in terms of $G^r, H^r$ and $G^r*H^r$, when $*$ is the join, Cartesian, symmetric difference, disjunctive, composition, skew and corona product. Then we solve the equation $(G*H)^r=G^r*H^r$. We also compute the Wiener index and Wiener polarity index of the skew product.

let g be a connected simple (molecular) graph. the distance d(u, v) between two vertices u and v of g is equal to the length of a shortest path that connects u and v. in this paper we compute some distance based topological indices of h-phenylenic nanotorus. at first we obtain an exactformula for the wiener index. as application we calculate the schultz index and modified schultz index of this ...

Topological indices have important role in theoretical chemistry for QSPR researches. Among the all topological indices the Randić and the Zagreb indices have been used more considerably than any other topological indices in chemical and mathematical literature. Most of the topological indices as in the Randić and the Zagreb indices are based on the degrees of the vertices of a connected graph....

For any simple connected undirected graph, it is well known that the Kirchhoff and multiplicative degree-Kirchhoff indices can be computed using the Laplacian matrix. We show that the same is true for the additive degree-Kirchhoff index and give a compact Matlab program that computes all three Kirchhoffian indices with the Laplacian matrix as the only input.

Let G be a connected simple (molecular) graph. The distance d(u, v) between two vertices u and v of G is equal to the length of a shortest path that connects u and v. In this paper we compute some distance based topological indices of H-Phenylenic nanotorus. At first we obtain an exact formula for the Wiener index. As application we calculate the Schultz index and modified Schultz index of this...

The Wiener index is a graph invariant that has found extensive application in chemistry. In addition to that a generating function, which was called the Wiener polynomial, who’s derivate is a q-analog of the Wiener index was defined. In an article, Sagan, Yeh and Zhang in [The Wiener Polynomial of a graph, Int. J. Quantun Chem., 60 (1996), 959969] attained what graph operations do to the Wiene...

In this note, we obtain the expressions for multiplicative Zagreb indices and coindices of derived graphs such as a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph and paraline graph.

todeschini et al. have recently suggested to consider multiplicative variants of additive graphinvariants, which applied to the zagreb indices would lead to the multiplicative zagrebindices of a graph g, denoted by ( ) 1  g and ( ) 2  g , under the name first and secondmultiplicative zagreb index, respectively. these are define as  ( )21 ( ) ( )v v gg g d vand ( ) ( ) ( )( )2 g d v d v gu...

The concept of geometric-arithmetic indices (GA) was put forward in chemical graph theory very recently. In spite of this, several works have already appeared dealing with these indices. In this paper we present lower and upper bounds on the second geometric-arithmetic index (GA2) and characterize the extremal graphs. Moreover, we establish Nordhaus-Gaddum-type results for GA2.