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.

Topological indices have important role in theoretical chemistry for QSPR researches. Among the all topological indices the Randić and the Zagreb indices have been used more considerably than any other topological indices in chemical and mathematical literature. Most of the topological indices as in the Randić and the Zagreb indices are based on the degrees of the vertices of a connected graph....

the first zagreb index, $m_1(g)$, and second zagreb index, $m_2(g)$, of the graph $g$ is defined as $m_{1}(g)=sum_{vin v(g)}d^{2}(v)$ and $m_{2}(g)=sum_{e=uvin e(g)}d(u)d(v),$ where $d(u)$ denotes the degree of vertex $u$. in this paper, the firstand second maximum values of the first and second zagreb indicesin the class of all $n-$vertex tetracyclic graphs are presented.

1 Hvar Observatory, Faculty of Geodesy, University of Zagreb, Kačićeva 26, HR-10000 Zagreb, Croatia 2 Kiepenheuer-Institut für Sonnenphysik, Schöneckstr. 6, D-79104 Freiburg, Germany 3 Geophysical Institute, Faculty of Science, University of Zagreb, Horvatovac bb, HR-10000 Zagreb, Croatia 4 Easy Toolkit, Inc., Houston, Texas, USA 5 Observatoire Royal de Belgique, Ave. Circulaire 3, B-1180 Bruxe...

1 Clinical Department for Clinical and Molecular Microbiology, University Hospital Center Zagreb, 10000 Zagreb, Croatia 2 Department of Microbiology, School of Medicine, University of Zagreb, 10000 Zagreb, Croatia 3 Department of Microbiology, University Hospital Center Split, 21000 Split, Croatia 4Cantonal Public Health Institute Zenica, 72000 Zenica, Bosnia and Herzegovina 5 Department for Sa...

J. Mlinarec1, Z. Šatović2, N. Malenica1, I. Ivančić-Baće1 and V. Besendorfer1,* Faculty of Science, University of Zagreb, Division of Biology, Department of Molecular Biology, Horvatovac 102a, HR-10000 Zagreb, Croatia and Department of Seed Science and Technology, Faculty of Agriculture, University of Zagreb, Svetošimunska 25, HR-10000 Zagreb, Croatia * For correspondence. E-mail [email protected]...

in this paper we give sharp upper bounds on the zagreb indices and characterize all trees achieving equality in these bounds. also, we give lower bound on first zagreb coindex of trees.

We give sharp upper bounds on the Zagreb indices and lower bounds on the Zagreb coindices of chemical trees and characterize the case of equality for each of these topological invariants.

we give sharp upper bounds on the zagreb indices and lower bounds on the zagreb coindices of chemical trees and characterize the case of equality for each of these topological invariants.

1Division of Zoology, Department of biology, Faculty of science, University of Zagreb, rooseveltov trg 6, 10000 Zagreb, Croatia (*[email protected]) 2Division of botany, Department of biology, Faculty of science, University of Zagreb, Marulićev trg 20/II, 10000 Zagreb, Croatia 3National Museum Zadar, Natural History Department, Medulićeva 1, 23000 Zadar, Croatia (prirodoslovni.odjel@nm...