A new extension of the generalized topological indices (GTI) approach is carried out to represent “simple” and “composite” topological indices (TIs) in an unified way. This approach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randić connectivity indices are expressed by means of ...

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.

1Department of Pediatrics, University of Zagreb, School of Medicine, University Hospital Centre Zagreb, Zagreb, Croatia, 2Department of Obstetrics and Gynecology, University Hospital Merkur, Zagreb, Croatia, 3Department of Pediatric Surgery, University of Zagreb, School of Medicine, University Hospital Centre Zagreb, Zagreb, Croatia, 4Department of Anesthesiology, Mayo Clinic, 200 First St SW, ...

Recently, the first and second Zagreb indices are generalized into the variable Zagreb indices which are defined by M1(G) = ∑ u∈V (d(u))2λ and M2(G) = ∑ uv∈E (d(u)d(v)), where λ is any real number. In this paper, we prove that M1(G)/n M2(G)/m for all unicyclic graphs and all λ ∈ (−∞, 0]. And we also show that the relationship of numerical value between M1(G)/n and M2(G)/m is indefinite in the d...

We establish some bounds for the number of spanning trees of connected graphs in terms of the number of vertices (n), the number of edges (m), maximum vertex degree (Δ1), minimum vertex degree (δ), first Zagreb index (M 1), and Randić index (R -1).

The hyper-Zagreb index of a connected graph G, denoted by HM(G), is defined as HM(G) = ∑ uv∈E(G) [dG(u) + dG(v)] where dG(z) is the degree of a vertex z in G. In this paper, we study the hyper-Zagreb index of four operations on graphs.

the first ($pi_1$) and the second $(pi_2$) multiplicative zagreb indices of a connected graph $g$, with vertex set $v(g)$ and edge set $e(g)$, are defined as $pi_1(g) = prod_{u in v(g)} {d_u}^2$ and $pi_2(g) = prod_{uv in e(g)} {d_u}d_{v}$, respectively, where ${d_u}$ denotes the degree of the vertex $u$. in this paper we present a simple approach to order these indices for connected graphs on ...

let $gamma_{n,kappa}$ be the class of all graphs with $ngeq3$ vertices and $kappageq2$ vertex connectivity. denote by $upsilon_{n,beta}$ the family of all connected graphs with $ngeq4$ vertices and matching number $beta$ where $2leqbetaleqlfloorfrac{n}{2}rfloor$. in the classes of graphs $gamma_{n,kappa}$ and $upsilon_{n,beta}$, the elements having maximum augmented zagreb index are determined.

The second Zagreb index of a graph G is an adjacency-based topological index, which is defined as ∑uv∈E(G)(d(u)d(v)), where uv is an edge of G, d(u) is the degree of vertex u in G. In this paper, we consider the second Zagreb index for bipartite graphs. Firstly, we present a new definition of ordered bipartite graphs, and then give a necessary condition for a bipartite graph to attain the maxim...