In a study on the structure–dependency of the total π-electron energy from 1972, Trinajstić and one of the present authors have shown that it depends on the sums ∑ v∈V d(v) 2 and ∑ v∈V d(v) , where d(v) is the degree of a vertex v of the underling molecular graph G. The first sum was later named first Zagreb index and over the years became one of the most investigated graph–based molecular stru...

What is the ideological direction of the judges whom President George W. Bush has appointed to the bench during his first term? Until now we have had no quantitative, empirical data to respond to this query. Critics of the President, often liberal Democrats, have suggested that Bush’s judicial appointees are ultra-conservatives who are hostile to the interests of racial minorities, women, the e...

0

The rst Zagreb index of a graph is equal to the sum of the square of the vertex degrees of the graph and the forgotten topological index (Findex) of a graph is de ned as the sum of cubes of the vertex degrees of the graph. These parameters have applications in chemistry and drug structures. For any xed integer d ≥ 2, the d-ary tree is a rooted tree in which each node has no more than d children...

Topological indices are the mathematical tools that correlate the chemical structure with various physical properties, chemical reactivity or biological activity numerically. A topological index is a function having a set of graphs as its domain and a set of real numbers as its range. In QSAR/QSPR study, a prediction about the bioactivity of chemical compounds is made on the basis of physico-ch...

This article revisits the case of The State of Israel v Adolph Eichmann and calls for renewed attention to the analysis of universal jurisdiction in this early example of it. Precisely because the Israeli court’s notion of universal jurisdiction is foreign to contemporary readers, it provides fresh guidance on a doctrine that has recently gained enormous importance in global politics. The Eichm...

In political science the economic left-right dimension plays a central role. A growing body of evidence shows that the economic policy preferences of a large segment of citizens do not scale sufficiently. Using Mokken scale analysis, this study determines the causes of this phenomenon. Differences in the extent to which the economic policy preferences of citizens fit the left-right dimension ca...

In this paper we study lower bounds in a unified way for large family of topological indices, including the first variable Zagreb index M 1 ? . Our aim is to obtain sharp inequalities and characterize corresponding extremal graphs. The main results provide several vertex-degree-based indices. These are new even Zagreb, inverse forgotten