let g be a graph. the first zagreb m1(g) of graph g is defined as: m1(g) = uv(g) deg(u)2. in this paper, we prove that each even number except 4 and 8 is a first zagreb index of a caterpillar. also, we show that the fist zagreb index cannot be an odd number. moreover, we obtain the fist zagreb index of some graph operations.

The Zagreb indices are among the oldest and the most famous topological molecular structure-descriptors. The first Zagreb index is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index is equal to the sum of the products of the degrees of pairs of adjacent vertices of the respective graph. In this paper, we characterize the extremal graphs with maximal, sec...

Let G = (V,E) be a graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges, e = uv∈E(G), d(u) is degree of vertex u. Then the first Zagreb polynomial and the first Zagreb index Zg1(G,x) and Zg1(G) of the graph G are defined as ( ) ( ) ∑ u v u d v E G d x + ∈ and ( ) ( ) ∑ e u G v uv E d d = ∈ + respectively. Recently Ghorbani and Hosseinzadeh introduced the first Eccentric Z...

The Zagreb regimen, an abbreviated intramuscular schedule for rabies vaccination, was developed by I. Vodopija and colleagues of the Zagreb Institute of Public Health in Croatia in the 1980s. It was recommended by WHO as one of the intramuscular (IM) schedules for rabies vaccination in 2010. We reviewed the literature on the immunogenicity, safety, economic burden, and compliance of the Zagreb ...

Maria Feligini1*, Vlatka Cubric-Curik2, Pietro Parma1, Ino Curik3, Gian Franco Greppi1,4 and Giuseppe Enne1,5 Istituto Sperimentale Italiano »Lazzaro Spallanzani«, Laboratorio di Epigenomica Applicata (LEA), Via Giovanni XXIII, I-26900 Lodi, Italy Dairy Science Department, Faculty of Agriculture University of Zagreb, Sveto{imunska 25, HR-10 000 Zagreb, Croatia Animal Science Department, Faculty...

For a (molecular) graph, the first Zagreb index M1 is equal to the sum of squares of the vertex degrees, and the second Zagreb index M2 is equal to the sum of products of degrees of pairs of adjacent vertices. In this paper, we investigate Zagreb indices of bicyclic graphs with a given matching number. Sharp upper bounds for the first and second Zagreb indices of bicyclic graphs in terms of the...

Let G = (V, E), V {v1, v2,..., vn}, be a simple connected graph of order n and size m, without isolated vertices. Denote by d1 ? d2 ?... dn, di d(vi) sequence vertex degrees G. The general zeroth-order Randic index is defined as 0R?(G) ?ni =1 d?i, where an arbitrary real number. corresponding coindex via 0R??(G) ?ni=1(n?1?di)d?i. Some new bounds for the relationship between 0R??(G?) 0R???1(G?) ...

The aim of this study was to determine the levels of six polychlorinated biphenyls (referred to as PCB-28, PCB-52, PCB-101, PCB-138, PCB-153 and PCB-180, according to the IUPAC) in freshwater fish from the Zagreb area. A total of 216 samples was collected from five sites: from the Sava River upstream of Zagreb, in Zagreb, and downstream of Zagreb, from Lake Jarun, and from five fishponds from t...