Some properties of the Zagreb indices

Some Observations on Comparing Zagreb Indices

Let G be a simple graph possessing n vertices and m edges. Let di be the degree of the i-th vertex of G , i = 1, . . . , n . The first Zagreb index M1 is the sum of d 2 i over all vertices of G . The second Zagreb index M2 is the sum di dj over pairs of adjacent vertices of G . In this paper we search for graph for which M1/n = M2/m , and show how numerous such graphs can be constructed. In add...

Some Classes of Graphs (dis)satisfying the Zagreb Indices Inequality

Recently Hansen and Vukičević [10] proved that the inequality M1/n ≤ M2/m, where M1 and M2 are the first and second Zagreb indices, holds for chemical graphs, and Vukičević and Graovac [17] proved that this also holds for trees. In both works is given a distinct counterexample for which this inequality is false in general. Here, we present some classes of graphs with prescribed degrees, that sa...

The first and second Zagreb indices of some graph operations

Comparing the Zagreb Indices

Let G = (V,E) be a simple graph with n = |V | vertices and m = |E| edges; let d1, d2, . . . , dn denote the degrees of the vertices of G. If ∆ = max i di ≤ 4, G is a chemical graph. The first and second Zagreb indices are defined as M1 = ∑

Multiplicative Zagreb Indices and Coindices of Some Derived Graphs

In this note, we obtain the expressions for multiplicative Zagreb indices and coindices of derived graphs such as a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph and paraline graph.