For a nontrivial graph G, its first Zagreb coindex is defined as the sum of degree sum over all non-adjacent vertex pairs in G and the second Zagreb coindex is defined as the sum of degree product over all non-adjacent vertex pairs in G. Till now, established results concerning Zagreb coindices are mainly related to composite graphs and extremal values of some special graphs. The existing liter...

The second Zagreb coindex is a well-known graph invariant defined as the total degree product of all non-adjacent vertex pairs in a graph. The second Zagreb eccentricity coindex is defined analogously to the second Zagreb coindex by replacing the vertex degrees with the vertex eccentricities. In this paper, we present exact expressions or sharp lower bounds for the second Zagreb eccentricity co...

In this note, we give expressions for the first(second) Zagreb coindex, second Zagreb index(coindex), third Zagreb index and first hyper-Zagreb index of the line graphs of subdivision graphs of 2D-lattice, nanotube and nanotorus of TUC4C8[p, q] and obtain upper bounds for Wiener index and degree-distance index of these graphs. This note continue the program of computing certain topological indi...

‎the second multiplicative zagreb coindex of a simple graph $g$ is‎ ‎defined as‎: ‎$${overline{pi{}}}_2left(gright)=prod_{uvnotin{}e(g)}d_gleft(uright)d_gleft(vright),$$‎ ‎where $d_gleft(uright)$ denotes the degree of the vertex $u$ of‎ ‎$g$‎. ‎in this paper‎, ‎we compare $overline{{pi}}_2$-index with‎ ‎some well-known graph invariants such as the wiener index‎, ‎schultz‎ ‎index‎, ‎eccentric co...

For a (molecular) graph, the hyper Zagreb index is defined as HM(G) = ∑ uv∈E(G) (dG(u) + dG(v)) 2 and the hyper Zagreb coindex is defined asHM(G) = ∑ uv/ ∈E(G) (dG(u)+dG(v)) 2. In this paper, the hyper Zagreb indices and its coindices of edge corona product graph, double graph and Mycielskian graph are obtained.

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.

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.

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.

For a nontrivial graph G, its first and second Zagreb coindices are defined [1], respectively, as M1(G) = ∑ uv ∈E(G) (dG(u)+dG(v)) and M2(G) = ∑ uv ∈E(G) dG(u)dG(v), where dG(x) is the degree of vertex x in G. In this paper, we obtained some new properties of Zagreb coindices. We mainly give explicit formulae for the first Zagreb coindex of line graphs and total graphs. Mathematics Subject Clas...

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...