an alexandroff topology on graphs
نویسندگان
چکیده
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 elementary step toward investigation of some properties of locally finite graphs by their corresponding topology which we introduce in this paper.
منابع مشابه
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...
متن کاملAn 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 intersection of each family of open sets is open. Then we investigate some properties of this topology. Our motivation is to give an elem...
متن کاملAlexandroff Theorem in Hausdorff Topology for Null-null-additive Set Multifunctions
In this paper we further a previous study concerning abstract regularity for monotone set multifunctions, with has immediate applications in well-known situations such as the Borel σ-algebra of a Hausdorff space and/or the Borel (Baire, respectively) δ-ring or σ-ring of a locally compact Hausdorff space. We also study relationships among abstract regularities and other properties of continuity....
متن کاملOn the topology of vertex-transitive graphs
The undirected graphs atoms were introduced independently Mader[21] and Watkins [28] in order to show that the connectivity of a connected undirected vertex-transitive is large. The directed graphs atoms were introduced by Chaty in [3]. The author obtained a structure Theorem for the atoms in the last case [9], showing that the connectivity of a connected vertex-transitive directed is large. Th...
متن کاملThe 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 ...
متن کاملTopology-Hiding Computation on All Graphs
A distributed computation in which nodes are connected by a partial communication graph is called topology-hiding if it does not reveal information about the graph beyond what is revealed by the output of the function. Previous results have shown that topology-hiding computation protocols exist for graphs of constant degree and logarithmic diameter in the number of nodes [Moran-OrlovRichelson, ...
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
bulletin of the iranian mathematical societyناشر: iranian mathematical society (ims)
ISSN 1017-060X
دوره 39
شماره 4 2013
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023