For a graph $G$ with edge set $E(G)$, the multiplicative sum Zagreb index of $G$ is defined as$Pi^*(G)=Pi_{uvin E(G)}[d_G(u)+d_G(v)]$, where $d_G(v)$ is the degree of vertex $v$ in $G$.In this paper, we first introduce some graph transformations that decreasethis index. In application, we identify the fourteen class of trees, with the first through fourteenth smallest multiplicative sum Zagreb ...

The aim of this investigation was to determine the levels of heavy metals and metalloids in freshwater fish from the Zagreb area. A total of 216 freshwater fish samples from 5 sites were examined: Sava river upstream from Zagreb, Sava river at Zagreb, Sava river downstream from Zagreb, Jarun Lake, and 5 "ecologic" fishponds from the Zagreb surroundings. The metals lead, cadmium, mercury and the...

The aim of this paper is to determine the differences in the outpatient consumption of cardiovascular drugs between Croatian regions: the City of Zagreb and Lika-Senj County. The data on the number of packages and the purchase price for each drug have been obtained from all pharmacies in Lika-Senj County and all pharmacies in the City of Zagreb. Defined daily doses/1000 inhabitants/day (DDD/100...

Tatjana Vilibić-Čavlek1, Iva Pem-Novosel2, Ira Gjenero-Margan2, Nenad Pandak3, Ljiljana Perić4, Ljubo Barbić5, Karlo Kožul6, Eddy Listeš7, Pavle Jeličić8, Vladimir Stevanović5, Giovanni Savini9 1Department of Virology, Croatian National Institute of Public Health; School of Medicine University of Zagreb; 2Epidemiology Service, Croatian National Institute of Public Health, Zagreb; 3Department of...

For a simple graph G with n vertices and m edges, the inequality M1(G)/n ≤ M2(G)/m, where M1(G) and M2(G) are the first and the second Zagreb indices of G, is known as Zagreb indices inequality. Generalization of these indices gives first M1(G) and second M2(G) variable Zagreb indices. Vukičević in [13] has given an incomplete proof for the claim: for all simple graphs and all λ ∈ [0, 12 ], hol...

We investigate the Zagreb index, one of the topological indices, of random recursive trees in this paper. Through a recurrence equation, the first two moments of Zn, the Zagreb index of a random recursive tree of size n, are obtained. We also show that the random process {Zn − E[Zn], n ≥ 1} is a martingale. Then the asymptotic normality of the Zagreb index of a random recursive tree is given by...

Recently two new degree concepts have been defined in graph theory: ev-degree and ve-degree. Also the evdegree and ve-degree Zagreb and Randić indices have been defined very recently as parallel of the classical definitions of Zagreb and Randić indices. It was shown that ev-degree and ve-degree topological indices can be used as possible tools in QSPR researches . In this paper we define the ve...

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 ...

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...