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 define and obtain several properties of the (adjacency) energy a hypergraph. particular, bounds for are obtained as functions structural spectral parameters, such Zagreb index radius. We also study how hypergraph varies when vertex/edge is removed or an edge divided. addition, solve extremal problem class hyperstars, show that never odd number.

In this paper, the edge a-Zagreb indices and its coindices of some graph operations, such as generalized hierarchical product, Cartesian Product, join, composition of two graphs are obtained. Using the results obtained here, we deduce the F -indices and its coindices for the above graph operation. Finally, we have computed the edge a-Zagreb Index, F -index and their coindices of some important ...

The edge version of traditional first Zagreb index is known as first reformulated Zagreb index. In this paper, we analyze and compare various lower and upper bounds for the first reformulated Zagreb index and we propose new lower and upper bounds which are stronger than the existing and recent results [Appl. Math. Comp. 273 (2016) 16-20]. In addition, we prove that our bounds are superior in co...

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...

Let G be a simple connected molecular graph with vertex set V(G) and edge set E(G). One important modification of classical Zagreb index, called hyper Zagreb index HM(G) is defined as the sum of squares of the degree sum of the adjacent vertices, that is, sum of the terms 2 [ ( ) ( )] G G d u d v  over all the edges of G, where ( ) G d u denote the degree of the vetex u of G. In this paper, th...

Let k ≥ 2 be an integer, a k-decomposition (G1,G2, . . . ,Gk) of the complete graph Kn is a partition of its edge set to form k spanning subgraphs G1,G2, . . . ,Gk. In this contribution, we investigate the Nordhaus–Gaddum-type inequality of a k-decomposition of Kn for the general Zagreb index and a 2-decomposition for the Zagreb co-indices, respectively. The corresponding extremal graphs are ch...

The first general Zagreb index is defined as Mλ 1 (G) = ∑ v∈V (G) dG(v) λ where λ ∈ R − {0, 1}. The case λ = 3, is called F-index. Similarly, reformulated first general Zagreb index is defined in terms of edge-drees as EMλ 1 (G) = ∑ e∈E(G) dG(e) λ and the reformulated F-index is RF (G) = ∑ e∈E(G) dG(e) 3. In this paper, we compute the reformulated F-index for some graph operations.

For a (molecular) graph G with vertex set V (G) and edge set E(G), the first Zagreb index of G is defined as M1(G) = ∑ v∈V (G) dG(v) 2 where dG(v) is the degree of vertex v in G. The alternative expression for M1(G) is ∑ uv∈E(G)(dG(u)+dG(v)). Very recently, Eliasi, Iranmanesh and Gutman [7] introduced a new graphical invariant ∏∗ 1(G) = ∏ uv∈E(G)(dG(u) + dG(v)) as the multiplicative version of ...