The first reformulated Zagreb index $EM_1(G)$ of a simple graph $G$ is defined as the sum of the terms $(d_u+d_v-2)^2$ over all edges $uv$ of $G .$ In this paper, the various upper and lower bounds for the first reformulated Zagreb index of a connected graph interms of other topological indices are obtained.

Topological indices are widely used as mathematical tools to analyze different types of graphs emerged in a broad range of applications. The Hyper-Zagreb index (HM) is an important tool because it integrates the first two Zagreb indices. In this paper, we characterize the trees and unicyclic graphs with the first four and first eight greatest HM-value, respectively.

The first general Zagreb index is defined as $M_1^lambda(G)=sum_{vin V(G)}d_{G}(v)^lambda$. The case $lambda=3$, is called F-index. Similarly, reformulated first general Zagreb index is defined in terms of edge-drees as $EM_1^lambda(G)=sum_{ein E(G)}d_{G}(e)^lambda$ and the reformulated F-index is $RF(G)=sum_{ein E(G)}d_{G}(e)^3$. In this paper, we compute the reformulated F-index for some grap...

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 ...

In mathematical chemistry, a particular attention is given to degree-based graph invariant. The Zagrebpolynomial is one of the degree based polynomials considered in chemical graph theory. A dendrimer isan artificially manufactured or synthesized molecule built up from branched units called monomers. Inthis note, the first, second and third Zagreb poly...

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...