The rst Zagreb index of a graph is equal to the sum of the square of the vertex degrees of the graph and the forgotten topological index (Findex) of a graph is de ned as the sum of cubes of the vertex degrees of the graph. These parameters have applications in chemistry and drug structures. For any xed integer d ≥ 2, the d-ary tree is a rooted tree in which each node has no more than d children...

the padmakar-ivan (pi) index is a wiener-szeged-like topological index which reflectscertain structural features of organic molecules. the pi index of a graph g is the sum of alledges uv of g of the number of edges which are not equidistant from the vertices u and v. inthis paper we obtain the second and third extremals of catacondensed hexagonal systems withrespect to the pi index.

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.

A {it topological index} of a graph is a real number related to the graph; it does not depend on labeling or pictorial representation of a graph. In this paper, we present the upper bounds for the product version of reciprocal degree distance of the tensor product, join and strong product of two graphs in terms of other graph invariants including the Harary index and Zagreb indices.

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, and let $d_u$ denote the degree of vertex $u$ in $G$. The Randi'c index of $G$ is defined as${R}(G) =sum_{uvin E(G)} 1/sqrt{d_ud_v}.$In this paper, we investigate the relationships between Randi'cindex and several topological indices.

Let $G=(V,E)$ be a simple connectedgraph with $n$ vertices, $m$ edges and sequence of vertex degrees$d_1 ge d_2 ge cdots ge d_n>0$, $d_i=d(v_i)$, where $v_iin V$. With $isim j$ we denote adjacency ofvertices $v_i$ and $v_j$. The generalsum--connectivity index of graph is defined as $chi_{alpha}(G)=sum_{isim j}(d_i+d_j)^{alpha}$, where $alpha$ is an arbitrary real<b...

The recent discovery of boron triangular nanotubes competes with carbon in many respects. The closed form of M-polynomial of nanotubes produces closed forms of many degree-based topological indices which are numerical parameters of the structure and, in combination, determine properties of the concerned nanotubes. In this report, we give M-polynomials of boron triangular nanotubes and recover m...

In this paper, we present some inequalities for the Co-PI index involving the some topological indices, the number of vertices and edges, and the maximum degree. After that, we give a result for trees. In addition, we give some inequalities for the largest eigenvalue of the Co-PI matrix of G.

The forgotten topological coindex (also called Lanzhou index) is defined for a simple connected graph G as the sum of the terms du2+dv2 over all non-adjacent vertex pairs uv of G, where du denotes the degree of the vertex u in G. In this paper, we present some inequalit...

In this article, a Quantitative structure Toxicity Relationships (QSTR) of twenty five phenol derivatives is presented. The QSTR study is mainly based on topological parameter. The topological parameter has been evaluated by CAChe prosoftware. The calculations of topological parameters have been done by MOPAC 2007. The statistical parameter has been calculated by SSP software. Various QSTR mode...