the vertex-edge wiener index of a simple connected graph g is defined as the sum of distances between vertices and edges of g. two possible distances d_1(u,e|g) and d_2(u,e|g) between a vertex u and an edge e of g were considered in the literature and according to them, the corresponding vertex-edge wiener indices w_{ve_1}(g) and w_{ve_2}(g) were introduced. in this paper, we present exact form...

The fact that the properties of a molecule are tightly connected to its structural  characteristics  is one of the fundamental concepts in chemistry. In this connection,  graph theory has been successfully applied in developing some relationships between topological indices and some thermodynamic properties. So ,  a novel method for computing the new descriptors to construct a quantitative rela...

Design of crystal-like lattices can be achieved by using some net operations. Hypothetical networks, thus obtained, can be characterized in their topology by various counting polynomials and topological indices derived from them. The networks herein presented are related to the Dyck graph and described in terms of Omega polynomial and PIv polynomials.

Wiener index is a topological index based on distance between every pair of vertices in a graph G. It was introduced in 1947 by one of the pioneer of this area e.g, Harold Wiener. In the present paper, by using a new method introduced by klavžar we compute the Wiener and Szeged indices of some nanostar dendrimers.

An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [dij], where for ij, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for distinct nuclei. Balaban introduced some monster graphs and then Randic computed complexit...

In this paper, we mainly consider the Hamiltonian indices of three classes graphs obtained from Petersen graph, that is, minimum integer m m-time iterated line graph Lm(G) these such is Hamiltonian. We show those by replacing every vertex with a n-cycle or complete order n, adding n pendant edges to each are both 2. addition, also study situations an edge and obtain their

‎let $d_{n,m}=big[frac{2n+1-sqrt{17+8(m-n)}}{2}big]$ and‎ ‎$e_{n,m}$ be the graph obtained from a path‎ ‎$p_{d_{n,m}+1}=v_0v_1 cdots v_{d_{n,m}}$ by joining each vertex of‎ ‎$k_{n-d_{n,m}-1}$ to $v_{d_{n,m}}$ and $v_{d_{n,m}-1}$‎, ‎and by‎ ‎joining $m-n+1-{n-d_{n,m}choose 2}$ vertices of $k_{n-d_{n,m}-1}$‎ ‎to $v_{d_{n,m}-2}$‎. ‎zhang‎, ‎liu and zhou [on the maximal eccentric‎ ‎connectivity ind...

In this paper, we introduce the Hosoya-Spectral indices and the Hosoya information content of a graph. The first measure combines structural information captured by partial Hosoya polynomials and graph spectra. The latter is a graph entropy measure which is based on blocks consisting of vertices with the same partial Hosoya polynomial. We evaluate the discrimination power of these quantities by...

In this paper, we present the various upper and lower bounds for the product version of reciprocal degree distance in terms of other graph inavriants. Finally, we obtain the upper bounds for the product version of reciprocal degree distance of the composition, Cartesian product and double of a graph in terms of other graph invariants including the Harary index and Zagreb indices. .

The entropy of a graph was first introduced by Rashevsky [1] and Trucco [2] to interpret as the structural information content of the graph and serve as a complexity measure. In this paper, we first state a number of definitions of graph entropy measures and generalized graph entropies. Then we survey the known results about them from the following three respects: inequalities and extremal prop...