In this paper, we introduce the atom bond connectivity E-Banhatti index and sum of a graph. Also compute these newly defined indices for wheel graphs, friendship chain silicate networks, honeycomb networks nanotubes.

Let G be a simple connected graph of order n. The connectivity index Rα(G) of a graph G is the sum of the weights (d(u)d(v)) of all edges uv of G, where α is a real number (α 6= 0), and d(u) denotes the degree of the vertex u. In this paper, we present some new bounds for the connectivity index of a graph G in terms of the eigenvalues of the Laplacian matrix or adjacency matrix of the graph G, ...

let g be a connected simple (molecular) graph. the distance d(u, v) between two vertices u and v of g is equal to the length of a shortest path that connects u and v. in this paper we compute some distance based topological indices of h-phenylenic nanotorus. at first we obtain an exactformula for the wiener index. as application we calculate the schultz index and modified schultz index of this ...

Several different topological indices (the carbon number, the Wiener index, the Balaban dis­ tance sum connectivity index, the Randic molecular identification number, and the Randic molecular connectivity indices °/, 2%, 3̂ p and 3/ c) were employed in the correlation of the velocity of ultrasonic sound in a variety of alkane and alcohol species. Using linear regression analyses and published so...

the eccentricity connectivity index of a molecular graph g is defined as (g) = av(g)deg(a)ε(a), where ε(a) is defined as the length of a maximal path connecting a to othervertices of g and deg(a) is degree of vertex a. here, we compute this topological index forsome infinite classes of dendrimer graphs.

in this paper we present explicit formulas for the eccentric connectivity index of three classesof chain hexagonal cacti. further, it is shown that the extremal chain hexagonal cacti withrespect to the eccentric connectivity index belong to one of the considered types. some openproblems and possible directions of further research are mentioned in the concluding section.

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.

Three new distance—based topological indices are described; two of them, D and D1 (mean distance topological indices, for any graphs, and for acyclic graphs, respectively) have a modest discriminating ability but may be useful for correlations, e. g. with octane numbers. The third index, J (average distance sum connectivity) is the least degenerate single topological index proposed till now. Th...

In this paper, we obtain the upper and lower bounds on the eccen- tricity connectivity index of unicyclic graphs with perfect matchings. Also we give some lower bounds on the eccentric connectivity index of unicyclic graphs with given matching numbers.