The terminal Wiener index TW = TW (G) of a graph G is equal to the sum of distances between all pairs of pendent vertices of G . This distance–based molecular structure descriptor was put forward quite recently [I. Gutman, B. Furtula, M. Petrović, J. Math. Chem. 46 (2009) 522–531]. In this paper we report results on TW of thorn graphs. Also a method for calculation of TW of dendrimers is descri...

The Wiener index of a connected graph is the sum distances between all unordered pairs vertices. A Eulerian if its vertex degrees are even. In Gutman et al. (2014) authors proved that cycle unique maximising among graphs given order. They also conjectured for order n≥26 consisting on n−2 vertices and triangle share with second largest index. conjecture known to hold n≤25 exception six values. t...

Topological indices are the real number of a molecular structure obtained via molecular graph G. Topological indices are used for QSPR, QSAR and structural design in chemistry, nanotechnology, and pharmacology. Moreover, physicochemical properties such as the boiling point, the enthalpy of vaporization, and stability can be estimated by QSAR/QSPR models. In this study, the QSPR (Quantitative St...

Experience gained during the past 7 years with the prolonged administration of probenecid (Pascale, Dubin, and Hoffman, 1952; Talbott, 1953; Gutman and Yu, 1955; Bartels, 1955; Bauer and Singh, 1957) or of salicylates (Marson, 1953, 1954, 1955) has shown that continuous therapy with a uricosuric agent in effective doses, is the only practical method at present available for preventing the compl...

Introduced by Gutman in 2021, the Sombor index is a novel graph-theoretic topological descriptor possessing potential applications modeling of thermodynamic properties compounds. Let H k n be family graphs on order and number cutvertices having at least one cycle. In this paper, we present minimum indices n. The corresponding extremal have been characterized as well.

For a (molecular) graph G with vertex set V (G) and edge set E(G), the first Zagreb index of G is defined as M1(G) = ∑ v∈V (G) dG(v) 2 where dG(v) is the degree of vertex v in G. The alternative expression for M1(G) is ∑ uv∈E(G)(dG(u)+dG(v)). Very recently, Eliasi, Iranmanesh and Gutman [7] introduced a new graphical invariant ∏∗ 1(G) = ∏ uv∈E(G)(dG(u) + dG(v)) as the multiplicative version of ...

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...

The sum of distances between all pairs of vertices W (G) in a connected graph G as a graph invariant was first introduced by Wiener [9] in 1947. He observed a correlation between boiling points of paraffins and this invariant, which has later become known as Wiener index of a graph. Today, the Wiener index is one of the most widely used descriptors in chemical graph theory. Due to its strong co...

The atom-bond connectivity (ABC) index of a graph ( , ) G V E is defined as ( ) [ ( ) ( ) 2] / [ ( ) ( )] uv E ABC G d u d v d u d v , where ( ) d u denotes the degree of vertex u of G . This recently introduced molecular structure descriptor found interesting applications in the study of the thermodynamic stability of acyclic saturated hydrocarbons, and the strain energy of their cyclic congen...