The Schrödinger operator on graphs and topology

The Shrödinger operator on graphs and topology

We shall define a Schrödinger operator for a one-dimensional simplicial complex (a graph) 1 Γ without ends (that is, at least two and only finitely many edges meet at any vertex), which acts on functions of vertices T or edges R: (Lψ) T = T ′ b T :T ′ ψ T ′ (V) for L 0 = ∂∂ * , b T :T ′ = 1, b T :T ′ = −m T , Here the coefficients are real, symmetric, and non-zero only for nearest neighbours T ...

An Alexandroff topology on graphs

Let G = (V,E) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. In this paper, we associate a topology to G, called graphic topology of G and we show that it is an Alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. Then we investigate some properties of this topology. Our motivation is to give an e...

an alexandroff topology on graphs

let g = (v,e) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. in this paper, we associate a topology to g, called graphic topology of g and we show that it is an alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. then we investigate some properties of this topology. our motivation is to give an e...

Preclosure operator and its applications in general topology

In this paper, we show that a pointwise symmetric pre-isotonic preclosure function is uniquely determined the pairs of sets it separates. We then show that when the preclosure function of the domain is pre-isotonic and the pre-closure function of the codomain is pre-isotonic and pointwise-pre-symmetric, functions which separate only those pairs of sets which are already separated are precontinu...

Operator algebras and topology