This paper is concerned with the general atom-bond sum-connectivity index ABSγ, which a generalization of recently proposed index, where γ any real number. For connected graph G more than two vertices, number ABSγ(G) defined as sum (1−2(dx+dy)−1)γ over all edges xy G, dx and dy represent degrees vertices x y respectively. −10≤γ≤10, significance ABSγ examined on data set twenty-five benzenoid hy...

A connected graph G is said to be a cactus if any two cycles have at most one vertex in common. The multiplicative sum Zagreb index of the product degrees adjacent vertices G. In this paper, we introduce several transformations that are useful tools for study extremal properties index. Using these and symmetric structural representations some graphs, determine graphs having maximal with prescri...

function f: G  , with this property that f(G1) = f(G2) if G1 and G2 are isomorphic. There are several vertex distance-based and degree-based indices which introduced to analyze the chemical properties of molecule graph. For instance: Wiener index, PI index, Szeged index, geometric-arithmetic index, atom-bond connectivity index and general sum connectivity index are introduced to test the perf...

If G is a (molecular) graph with n vertices, and di is the degree of its i-th vertex, then the sum-connectivity index of G is the sum of the weights (du +dv)− 1 2 of all edges uv of G. A polyomino system is a finite 2-connected plane graph such that each interior face (or say a cell) is surrounded by a regular square of length one. Formulas for calculating the sum-connectivity index of polyomin...

We determine the minimum sum–connectivity index of bicyclic graphs with n vertices and matching number m, where 2 ≤ m ≤ ⌊n2 ⌋, the minimum and the second minimum, as well as the maximum and the second maximum sum–connectivity indices of bicyclic graphs with n ≥ 5 vertices. The extremal graphs are characterized. MSC 2000: 05C90; 05C35; 05C07

In this paper I shall show how certain bounds on the possible diagrams presenting a given oriented knot or link K can be found from its two-variable polynomial PK defined in [3]. The inequalities regarding exponent sum and braid index of possible representations of K by a closed braid which are proved in [5] and [2] follow as a special case. Notation. In a diagram D for an oriented knot, write ...