We derive sharp lower bounds for the first and the second Zagreb indices (M1 and M2 respectively) for trees and chemical trees with the given number of pendent vertices and find optimal trees. M1 is minimized by a tree with all internal vertices having degree 4, while M2 is minimized by a tree where each “stem” vertex is incident to 3 or 4 pendent vertices and one internal vertex, while the res...

In a study on the structure–dependency of the total π-electron energy from 1972, Trinajstić and one of the present authors have shown that it depends on the sums ∑ v∈V d(v) 2 and ∑ v∈V d(v) , where d(v) is the degree of a vertex v of the underling molecular graph G. The first sum was later named first Zagreb index and over the years became one of the most investigated graph–based molecular stru...

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...

This chapter deals with computation of viscosity of 35 alcohols at 20C with the computational tools Multi-linear Regression (MLR) and Associative Neural Network(ASNN) . The four descriptors are used which are variable Zagreb index, Number of Hydroxyl Groups(NOH), Molecular Weight (MW) and Number of Carbon atoms (Nc). MLR is used to optimize the parameter(λ) in the variable Zagreb index by minim...

a topological index of a molecular graph g is a numeric quantity related to g which isinvariant under symmetry properties of g. in this paper we obtain the randić, geometricarithmetic,first and second zagreb indices , first and second zagreb coindices of tensorproduct of two graphs and then the harary, schultz and modified schultz indices of tensorproduct of a graph g with complete graph of ord...

We give sharp upper bounds on the Zagreb indices and lower bounds on the Zagreb coindices of chemical trees and characterize the case of equality for each of these topological invariants.