Lexicographic metric spaces: Basic properties and the metric dimension
نویسندگان
چکیده
منابع مشابه
Basic Properties of Metric and Normed Spaces
1 Definitions and Examples 1.1 Metric and Normed Spaces Definition 1.1. A metric space is a pair (X, d), where X is a set and d is a function from X ×X to R such that the following conditions hold for every x, y, z ∈ X. 1. Non-negativity: d(x, y) ≥ 0. 2. Symmetry: d(x, y) = d(y, x). 3. Triangle inequality: d(x, y) + d(y, z) ≥ d(x, y) . 4. d(x, y) = 0 if and only if x = y. Elements of X are call...
متن کاملThe metric dimension of the lexicographic product of graphs
A set of vertices W resolves a graph G if every vertex is uniquely determined by its coordinate of distances to the vertices in W . The minimum cardinality of a resolving set of G is called themetric dimension of G. In this paper, we consider a graphwhich is obtained by the lexicographic product between two graphs. The lexicographic product of graphs G and H , which is denoted by G ◦ H , is the...
متن کاملThe metric dimension and girth of graphs
A set $Wsubseteq V(G)$ is called a resolving set for $G$, if for each two distinct vertices $u,vin V(G)$ there exists $win W$ such that $d(u,w)neq d(v,w)$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. The minimum cardinality of a resolving set for $G$ is called the metric dimension of $G$, and denoted by $dim(G)$. In this paper, it is proved that in a connected graph $...
متن کاملCohomological Dimension Theory of Compact Metric Spaces
0. Introduction 1 1. General properties of the cohomological dimension 2 2. Bockstein theory 6 3. Cohomological dimension of Cartesian product 10 4. Dimension type algebra 15 5. Realization theorem 19 6. Test spaces 24 7. Infinite-dimensional compacta of finite cohomological dimension 28 8. Resolution theorems 33 9. Resolutions preserving cohomological dimensions 41 10. Imbedding and approximat...
متن کاملEmbedding Finite Metric Spaces in Low Dimension
This paper presents novel techniques that allow the solution to several open problems regarding embedding of finite metric spaces into Lp. We focus on proving near optimal bounds on the dimension with which arbitrary metric spaces embed into Lp. The dimension of the embedding is of very high importance in particular in applications and much effort has been invested in analyzing it. However, no ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applicable Analysis and Discrete Mathematics
سال: 2020
ISSN: 1452-8630,2406-100X
DOI: 10.2298/aadm180627004r