Chemical compounds and drugs are often modelled as graphs where each vertex represents an atom of molecule, and covalent bounds between atoms are represented by edges between the corresponding vertices. This graph derived from a chemical compounds is often called its molecular graph, and can be different structures. In this paper, by virtue of mathematical derivation, we determine the fourth, f...

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, ...

Zagreb University Hospital Center, School of Medicine, University of Zagreb, Clinical Department of Dermatology and Venereology, Zagreb, 1Čakovec General Hospital, Dermatovenereology Unit, Čakovec, 2Zagreb University Hospital Center, School of Medicine, University of Zagreb, Department of Nephrology, Arterial Hypertension, Dialysis and Transplantation and 3Zagreb University Hospital Center, Dep...

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).

A class of graph invariants referred to today as topological indices are inefficient progressively acknowledged by scientific experts and others be integral assets in the depiction structural phenomena. The structure an interconnection network can represented a graph. In network, vertices represent processor nodes edges links between nodes. Graph play vital feature theory distinguish properties...

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 Atom-bond-connectivity index ABC of a graph G is determined by d_i and d_j. In this paper, sharp results for the general which has chemical applications are found using different methods. These new inex investigated in terms its edges, vertices degrees. particular, some relations obtained involving topological indices; Randic index, Zagreb Harmonic Narumi-Katayama index. Indeed, improved he...