In this paper, the effects on the first general Zagreb index are observed when some operations, such as edge moving, edge separating and edge switching are applied to the graphs. Moreover, we obtain the majorization theorem to the first general Zagreb indices between two graphic sequences. Furthermore, we illustrate the application of these new properties, and obtain the largest or smallest fir...

in this paper, we determine the degree distance of the complement of arbitrary mycielskian graphs. it is well known that almost all graphs have diameter two. we determine this graphical invariant for the mycielskian of graphs with diameter two.

For a (molecular) graph, the multiplicative Zagreb indices ∏ 1-index and ∏ 2index are multiplicative versions of the ordinary Zagreb indices (M1-index and M2index). In this note we report several sharp upper bounds for ∏ 1-index in terms of graph parameters including the order, size, radius, Wiener index and eccentric distance sum, and upper bounds for ∏ 2-index in terms of graph parameters inc...

in this paper we give sharp upper bounds on the zagreb indices and characterize all trees achieving equality in these bounds. also, we give lower bound on first zagreb coindex of trees.

For a (molecular) graph, the first Zagreb index M1 is equal to the sum of squares of the vertex degrees, and the second Zagreb index M2 is equal to the sum of products of degrees of pairs of adjacent vertices. In this paper, we investigate Zagreb indices of bicyclic graphs with a given matching number. Sharp upper bounds for the first and second Zagreb indices of bicyclic graphs in terms of the...

The reformulated Zagreb indices of a graph is obtained from the classical Zagreb by replacing vertex degree by edge degree and are defined as sum of squares of the degree of the edges and sum of product of the degrees of the adjacent edges. In this paper we give some explicit results for calculating the first and second reformulated Zagreb indices of dendrimers. Mathematics Subject Classificati...

The Zagreb indices are the oldest graph invariants used in mathematical chemistry to predict the chemical phenomena. In this paper we define the multiple versions of Zagreb indices based on degrees of vertices in a given graph and then we compute the first and second extremal graphs for them.

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.

Todeschini et al. have recently suggested to consider multiplicative variants of additive graph invariants, which applied to the Zagreb indices would lead to the multiplicative Zagreb indices of a graph G, denoted by ( ) 1  G and ( ) 2  G , under the name first and second multiplicative Zagreb index, respectively. These are define as     ( ) 2 1 ( ) ( ) v V G G G d v and ( ) ( ) ( ) ( ) 2...