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...

The first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices of the respective graph. In this paper we present the lower bound on M1 and M2 among all unicyclic graphs of given order, maximum degree, and cycle length, and characterize graphs for which th...

P. Pervan,1,* P. Lazić,2,4,† M. Petrović,1 I. Šrut Rakić,1 I. Pletikosić,1 M. Kralj,1,4 M. Milun,1 and T. Valla3 1Institut za fiziku, Bijenička 46, HR-10000, Zagreb, Croatia, 2Institut Ruđer Bošković, Bijenička 54, 10000, Zagreb, Croatia, 3Department of Condensed Matter Physics & Materials Science, Brookhaven National Laboratory, Upton, New York 11973, USA 4Center of Excellence for Advanced Mat...

Let G = (V,E), V {1,2,...,n}, be a simple connected graph of order n, size m with vertex degree sequence d1 ? d2 ... dn > 0, di d(vi). The geometric-arithmetic topological index is defined as GA(G) i~j 2? didj/di+dj, whereas the coindex GA?(G) i~/j 2 didj/di+dj . New lower bounds for and in terms some parameters other invariants are obtained.

For a simple graph G with n vertices and m edges, the first Zagreb index and the second Zagreb index are defined as M1(G) = ∑ v∈V d(v) 2 and M2(G) = ∑ uv∈E d(u)d(v). In [34], it was shown that if a connected graph G has maximal degree 4, then G satisfies M1(G)/n = M2(G)/m (also known as the Zagreb indices equality) if and only if G is regular or biregular of class 1 (a biregular graph whose no ...

The authors Miličević et al. introduced the reformulated Zagreb indices [1], which is a generalization of classical Zagreb indices of chemical graph theory. In this paper, we mainly consider the maximum and minimum for the first reformulated index of graphs with connectivity at most k. The corresponding extremal graphs are characterized.

Tricaine methane-sulfonate (MS-222) application in fish anaesthesia By N. Topic Popovic, I. Strunjak-Perovic, R. Coz-Rakovac, J. Barisic, M. Jadan, A. Persin Berakovic and R. Sauerborn Klobucar Laboratory of Ichthyopathology – Biological Materials, Division for Materials Chemistry, Rudjer Boskovic Institute, Zagreb, Croatia; Department of Anaesthesiology, University Hospital Clinic, Zagreb, Cro...