The Randić index of a graph G, written R(G), is the sum of 1 √ d(u)d(v) over all edges uv in E(G). Let d and D be positive integers d < D. In this paper, we prove that if G is a graph with minimum degree d and maximum degree D, then R(G) ≥ √ dD d+Dn; equality holds only when G is an n-vertex (d,D)-biregular. Furthermore, we show that if G is an n-vertex connected graph with minimum degree d and...

Let G be a (molecular) graph with vertex set V 1⁄4 fv1;v2; . . . ;vng. Let dðv iÞ be the degree of the vertex v i 2 V . If the vertices v i1 ;v i2 ; . . . ;v ihþ1 form a path of length h;h P 1, in the graph G, then the hth order Randić index Rh of G is defined as the sum of the terms 1= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffif...

The consumer price index (CPI) is usually computed as a fixed-weighted Laspeyres price index, with the weights updated at discrete intervals only. It is well known that the Laspeyres functional form entails a substitution bias. One way to reduce it would be to use chained indices, and superlative ones if possible. Unfortunately, the necessary data are often missing. This paper proposes a simple...

We develop a new consistent conditional moment test of functional form based on nuisance parameter indexed sample moments. We reduce the nuisance parameter space to known countable sets, provide a new vantage into why existing parametric moment condition tests work, and uncover a new class of revealing weights. These results are exploited to construct a weighted average conditional moment test,...

The practice of making hedonic-based price adjustments to remove the effects of quality changes in goods and services that enter into the calculation of the U.S. Consumer Price Index (CPI) has to date focused primarily on indexes for consumer electronics, appliances, housing, and apparel. In an effort to expand the use of hedonic adjustments to a service-oriented area of the CPI, this article i...

the present note is devoted to establish some extremal results for the zeroth-order general randi'{c} index of cacti, characterize the extremal polyomino chains with respect to the aforementioned index, and hence to generalize two already reported results.