Using graph-theoretical techniques, we establish an inequality regarding the number of walks and closed walks in a graph. This inequality yields several upper bounds for the number of closed walks in a graph in terms of the number of vertices, number of edges, maximum degree, degree sequence, and the Zagreb indices of the graph. As applications, we also present some new upper bounds on the Estr...

AIM To investigate the prevalence of dental caries and treatment needs in schoolchildren aged 7-14 years from Zagreb. METHODS Dental examinations based on the World Health Organization criteria were performed on 1168 children in the period 2009-2010. The teeth were clinically examined with standard dental instruments using visual-tactile method under standard dental light. We recorded the cli...

Here we report horizontal symptomatic transmission of the Leningrad-Zagreb (L-Zagreb) mumps vaccine virus. Children who were the source of transmission had been vaccinated with the MMR vaccine (Serum Institute of India) contained L-Zagreb mumps virus. This is the first report of horizontal symptomatic transmission of this vaccine. The etiology of all seven contact cases was confirmed by epidemi...

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...

SUICIDE AS THE FIRST MANIFESTATION OF FIRST-EPISODE PSYCHOSIS IN 21-YEAR-OLD MAN: A CASE REPORT Maja Vilibić, Dario Bagarić, Branko Kolarić, Kresimir Radic, Marko Curković & Maja Zivkovic University Psychiatric Hospital Vrapce, Zagreb, Croatia Department for Social Medicine and Epidemiology, Medical School, University of Rijeka, Rijeka, Croatia Department of Epidemiology, Teaching Institute of ...

The forgotten topological coindex (also called Lanzhou index) is defined for a simple connected graph G as the sum of the terms du2+dv2 over all non-adjacent vertex pairs uv of G, where du denotes the degree of the vertex u in G. In this paper, we present some inequalit...

The first and second Hyper-Zagreb index of a connected graph $G$ is defined by $HM_{1}(G)=\sum_{uv \in E(G)}[d(u)+d(v)]^{2}$ $HM_{2}(G)=\sum_{uv E(G)}[d(u).d(v)]^{2}$. In this paper, the indices certain graphs are computed. Also bounds for determined. Further linear regression analysis degree based with boiling points benzenoid hydrocarbons carried out. model, on index, better than models corre...

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...

The reformulated Zagreb indices of a graph is obtained from the classical Zagreb by replacing vertex degree by edge degree and are defined as sum of squares of the degree of the edges and sum of product of the degrees of the adjacent edges. In this paper we give some explicit results for calculating the first and second reformulated Zagreb indices of dendrimers. Mathematics Subject Classificati...