Science is rich in abstract concepts that capture complex processes astonishingly simple ways. A prominent example the reduction of molecules to graphs. This work introduces a design principle for parametrized quantum circuits based on chemical graphs, providing way forward three major obstacles circuit molecular systems: Operator ordering, parameter initialization and initial state preparation...

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...

solvable graphs (also known as reachable graphs) are types of graphs that any arrangement of a specified number of agents located on the graph’s vertices can be reached from any initial arrangement through agents’ moves along the graph’s edges, while avoiding deadlocks (interceptions). in this paper, the properties of solvable graphs are investigated, and a new concept in multi agent moti...

Let E” be n-dimensional Euclidean space. A molecular space is a family of unit cubes in E”. Any molecular space can be represented by its intersection graph. Conversely, it is known that any graph G can be represented by molecular space M(G) in E” for some n. Suppose that S, and S, are topologically equivalent surfaces in E” and molecular spaces M, and M, are the two families of unit cubes inte...

The tenacity of an incomplete connected graph G is defined as T (G) = min{ |S|+m(G−S) ω(G−S) : S ⊂ V (G), ω(G− S) > 1}, where ω(G− S) and m(G− S), respectively, denote the number of components and the order of a largest component inG−S. This is a reasonable parameter to measure the vulnerability of networks, as it takes into account both the amount of work done to damage the network and how bad...

Topoi are known to be categories with extra properties that make them much alike the category of Sets. In a Topoi it is possible to define adequate notions of membership, elements and subobjects, power ”sets”, and finally, every Topoi has an internal logic able to justify any reasoning carried inside it. Most of the cases, this logic is not Classical (Boolean). The general logic for the Topoi i...

Article history: Available online 25 March 2011 Submitted by J.J. Loiseau AMS classification: 15A80 15A39 15A03

Graphs are suitable for describing the structure of complex systems and graph transformations for modeling their dynamic evolution. We are interested in a particular representation of molecular complexes as graphs and of reaction patterns as graph transformations: • the behavior of a protein is given by its functional domains / sites on the surface • two proteins can interact by binding or chan...