We introduce a partial order on the collection of chemical trees based on tree transformations. This partial order is tightly related to the Randić connectivity index χ. Its analysis provides new structural information about the behavior of χ. As an illustration of the approach presented, we give a different and more structural view of some known results about the first values of χ on the colle...

For a simple digraph G of order n with vertex set {v1, v2, . . . , vn}, let d+i and d − i denote the out-degree and in-degree of a vertex vi in G, respectively. Let D (G) = diag(d+1 , d + 2 , . . . , d + n ) and D−(G) = diag(d1 , d − 2 , . . . , d − n ). In this paper we introduce S̃L(G) = D̃(G)−S(G) to be a new kind of skew Laplacian matrix of G, where D̃(G) = D+(G)−D−(G) and S(G) is the skew-adj...

A new Skew Tolerant Flip-Flop (STFF) that achieves the lowest reported delay and energy-delay product while absorbing up to 54ps of clock skew is described. In addition, a method for characterizing clock skew absorbing flip-flops is presented. This comparison is apples-to-apples because the best previously reported flip-flops [1-4] are fabricated on the same wafer and measured using a common te...

We discuss some features of the orthogonalization methods commonly applied to QSPR QSAR studies. We outline the well known multivariable linear regression analysis in vector form in order to compare mainly Randic and Gram-Schmidt orthogonalization procedures and also cast the basis for other approaches like Löwdin’s one. We expect that present review may become the starting point for future dev...

Abstract. Topological indices are the numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. Graph theory is a delightful playground for the exploration of proof techniques in Discrete Mathematics and its results have applications in many areas of sciences. A graph is a ...

Let G be a collection of graphs with n vertices. We present a simple description of [G]χ = {H ∈ G : χ(H) = χ(G)} where χ denotes the Randić index. We associate to G a Q-linear map ρ : Qm → Qk (for some integers k, m depending on G) such that the kernel of ρ contains the necessary information to describe [G]χ in terms of linear equations. These results provide precise tools for analyzing the beh...

QSPR study on benzene derivatives have been made using recently introduced topological methodology. In this study the relationship between the Randic' (x'), Balaban (J), Szeged (Sz),Harary (H), Wiener (W), HyperWiener and Wiener Polarity (WP) to the thermal energy (Eth), heat capacity (CV) and entropy (S) of benzene derivatives is represented. Physicochemical properties are taken from the quant...