We find the extremal values of the energy, the Wiener index and several vertex-degree-based topological indices over the set of Kragujevac trees with the central vertex of fixed degree. 2010 Mathematics Subject Classification : 05C90, 05C35.

two sides of the edge e, and where the summation goes over all edges of T . The λ -modified Wiener index is defined as Wλ (T ) = ∑ e [nT,1(e) · nT,2(e)] . For each λ > 0 and each integer d with 3 ≤ d ≤ n− 2, we determine the trees with minimal λ -modified Wiener indices in the class of trees with n vertices and diameter d. The reverse Wiener index of a tree T with n vertices is defined as Λ (T)...

Let G be a graph. The distance d(u,v) between the vertices u and v of the graph G is equal to the length of a shortest path that connects u and v. The Wiener index W(G) is the sum of all distances between vertices of G, whereas the hyper-Wiener index WW(G) is defined as WW(G)=12W(G)+12@?"{"u","v"}"@?"V"("G")d (u,v)^2. In this paper the hyper-Wiener indices of the Cartesian product, composition,...

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...

In this paper, a novel eccentric neighborhood degree-based topological indices, termed Zagreb have been conceptualized and its discriminating power investigated with regard to the predictability of boiling point chemical substances. The indices was compared that Wiener connectivity indices. Some explicit results for those new some graphs graph operations such as join, disjunction, composition, ...

let $g$ be a molecular graph with vertex set $v(g)$, $d_g(u, v)$ the topological distance between vertices $u$ and $v$ in $g$. the hosoya polynomial $h(g, x)$ of $g$ is a polynomial $sumlimits_{{u, v}subseteq v(g)}x^{d_g(u, v)}$ in variable $x$. in this paper, we obtain an explicit analytical expression for the expected value of the hosoya polynomial of a random benzenoid chain with $n$ hexagon...

We derived explicit formulae for the eccentric connectivity index and Wiener index of 2-dimensional square-octagonal TUC4C8(R) lattices with open and closed ends. New compression factors for both indices are also computed in the limit N-->∞.

Every molecular structure can be regarded as a graph, and each graph can be transformed into characteristic scalar – topological index. There are many, over 1000 topological indices used by chemists, but they are not equally successful in solving specific problems. For the prediction of stability of coordination compounds valence molecular connectivity index of the 3rd order (χ) proved best. St...

Biological diversity, also known as biodiversity, is an important criterion for measuring the value of an ecosystem. As biodiversity is closely related to human welfare and quality of life, many efforts to restore and maintain the biodiversity of species have been made by government agencies and non-governmental organizations, thereby drawing a substantial amount of international attention. In ...

Abstract Many chemical indices have been invented in theoretical chemistry, such as Wiener index, Merrifield-Simmons index, Hosoya index, spectral radius and Randić index, etc. The extremal trees and unicyclic graphs for these chemical indices are interested in existing literature. Let G be a molecular graph (called a cacti), which all of blocks of G are either edges or cycles. Denote G (n, r) ...