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...

In this paper, we calculate the eccentric connectivity index and the eccentricity sequence of two infinite classes of fullerenes with 50 + 10k and 60 + 12k (k in N) carbon atoms.

we derived explicit formulae for the eccentric connectivity index and wiener index of2-dimensional square-octagonal tuc4c8(r) lattices with open and closed ends. newcompression factors for both indices are also computed in the limit n-->∞.

Here we study the normalized Laplacian characteristics polynomial (L-polynomial) for trees and specifically for starlike trees. We describe how the L-polynomial of a tree depends on some topological indices. For which, we also define the higher order general Randić indices for matching and which are different from higher order connectivity indices. Finally we provide the multiplicity of the eig...

If $G$ is a connected graph with vertex set $V$, then the eccentric connectivity index of $G$, $xi^c(G)$, is defined as $sum_{vin V(G)}deg(v)ecc(v)$ where $deg(v)$ is the degree of a vertex $v$ and $ecc(v)$ is its eccentricity. In this paper we show some convergence in probability and an asymptotic normality based on this index in random bucket recursive trees.

The generalized atom-bond connectivity index of a graph G is denoted by ABCa(G) and defined as the sum of weights ((d(u)+d(v)-2)/d(u)d(v))aa$ over all edges uv∊G. A cactus is a graph in which any two cycles have at most one common vertex. In this paper, we compute sharp bounds for  ABCa index for cacti of order $n$ ...

In this paper, we show that in the class of connected graphs G of order n ≥ 3 having girth at least equal to k, 3 ≤ k ≤ n, the unique graph G having minimum general sum-connectivity index χα(G) consists of Ck and n−k pendant vertices adjacent to a unique vertex of Ck, if−1 ≤ α < 0. This property does not hold for zeroth-order general Randić index Rα(G).

Let Sz(G), Sz(G) and W (G) be the Szeged index, revised Szeged index and Wiener index of a graph G. In this paper, the graphs with the fourth, fifth, sixth and seventh largest Wiener indices among all unicyclic graphs of order n > 10 are characterized; and the graphs with the first, second, third, and fourth largest Wiener indices among all bicyclic graphs are identified. Based on these results...