‎The Narumi-Katayama index was the first topological index defined‎ ‎by the product of some graph theoretical quantities‎. ‎Let $G$ be a ‎simple graph with vertex set $V = {v_1,ldots‎, ‎v_n }$ and $d(v)$ be‎ ‎the degree of vertex $v$ in the graph $G$‎. ‎The Narumi-Katayama ‎index is defined as $NK(G) = prod_{vin V}d(v)$‎. ‎In this paper,‎ ‎the Narumi-Katayama index is generalized using a $n$-ve...

The spectral graph theory explores connections between combinatorial features of graphs and algebraic properties associated matrices. neighborhood inverse sum indeg (NI) index was recently proposed explored to be a significant molecular descriptor. Our aim is investigate the NI from standpoint, for which suitable matrix proposed. symmetric since it generated edge connection information undirect...

The eccentric connectivity index ξ is a novel distance–based molecular structure descriptor that was recently used for mathematical modeling of biological activities of diverse nature. It is defined as ξ(G) = ∑ v∈V (G) deg(v) · ε(v) , where deg(v) and ε(v) denote the vertex degree and eccentricity of v , respectively. We survey some mathematical properties of this index and furthermore support ...

The search of molecular structures inside a large database of chemical compounds is a critical step for many computer programs used in several domains of chemistry. During the last years, the size of many chemical databases has dramatically increased, hence in the meantime, search engines needed to be more and more powerful. The speed and the efficiency of screening processes of the chemical co...

Molecular similarity is a pervasive concept in drug design. The basic idea underlying molecular similarity is the similar property principle, which states that structurally similar molecules will exhibit similar physicochemical and biological properties. In this paper, a new graph-based molecular descriptor (GBMD) is introduced. The GBMD is a new method of obtaining a rough description of 2D mo...

The isomorphism problem is not known to be NP-complete nor polynomial. Yet it is crucial when maintaining large conceptual graphs databases. Taking advantage of conceptual graphs speciicities, whenever, by means of structural functions, a linear order of the conceptual nodes of a conceptual graph G can be computed as invariant under automorphism, a descriptor is assigned to G in such a way that...

In this technical note, we discuss an algorithm for the computation of the L∞-norm of transfer functions related to descriptor systems. We show how one can achieve this goal by computing the eigenvalues of certain skew-Hamiltonian/Hamiltonian matrix pencils and analyze arising problems. We also formulate and prove a theoretical result which serves as a basis for testing a transfer function matr...