Determining Sets, Resolving Sets, and the Exchange Property
نویسندگان
چکیده
منابع مشابه
Determining Sets, Resolving Sets, and the Exchange Property
A subset U of vertices of a graph G is called a determining set if every automorphism of G is uniquely determined by its action on the vertices of U . A subset W is called a resolving set if every vertex in G is uniquely determined by its distances to the vertices of W . Determining (resolving) sets are said to have the exchange property in G if whenever S and R are minimal determining (resolvi...
متن کاملResolving Sets and Semi-Resolving Sets in Finite Projective Planes
In a graph Γ = (V,E) a vertex v is resolved by a vertex-set S = {v1, . . . , vn} if its (ordered) distance list with respect to S, (d(v, v1), . . . , d(v, vn)), is unique. A set A ⊂ V is resolved by S if all its elements are resolved by S. S is a resolving set in Γ if it resolves V . The metric dimension of Γ is the size of the smallest resolving set in it. In a bipartite graph a semi-resolving...
متن کاملDetermining sets
We give several constructions of determining sets in various settings. We also demonstrate the connections between determining sets, skew karcs and linear codes of minimum distance 5. 1. Motivation. Let P be a non-empty set of elements which we shall call points. Let B be a non-empty set of subsets of P which we shall call blocks. We consider the use of a point/block system S = (P, B) in a mess...
متن کاملCOUNTABLE COMPACTNESS AND THE LINDEL¨OF PROPERTY OF L-FUZZY SETS
In this paper, countable compactness and the Lindel¨of propertyare defined for L-fuzzy sets, where L is a complete de Morgan algebra. Theydon’t rely on the structure of the basis lattice L and no distributivity is requiredin L. A fuzzy compact L-set is countably compact and has the Lindel¨ofproperty. An L-set having the Lindel¨of property is countably compact if andonly if it is fuzzy compact. ...
متن کاملA convex combinatorial property of compact sets in the plane and its roots in lattice theory
K. Adaricheva and M. Bolat have recently proved that if $,mathcal U_0$ and $,mathcal U_1$ are circles in a triangle with vertices $A_0,A_1,A_2$, then there exist $jin {0,1,2}$ and $kin{0,1}$ such that $,mathcal U_{1-k}$ is included in the convex hull of $,mathcal U_kcup({A_0,A_1, A_2}setminus{A_j})$. One could say disks instead of circles.Here we prove the existence of such a $j$ and $k$ ...
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: Graphs and Combinatorics
سال: 2009
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-010-0880-6