Conditional resolvability in graphs: a survey
For an ordered set W={w1,w2,…,wk} of vertices and a vertex v in a connected graph G, the code of v with respect to W is the k-vector cW(v)=(d(v,w1),d(v,w2),…,d(v,wk)), where d(x,y) represents the distance between the vertices x and y. The set W is a resolving set for G if distinct vertices of G have...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204311403 |
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| Summary: | For an ordered set W={w1,w2,…,wk} of vertices and
a vertex v in a connected graph G, the code of v with
respect to W is the k-vector cW(v)=(d(v,w1),d(v,w2),…,d(v,wk)), where d(x,y) represents the distance
between the vertices x and y. The set W is a resolving set
for G if distinct vertices of G have distinct codes with
respect to W. The minimum cardinality of a resolving set for
G is its dimension dim(G). Many resolving parameters are
formed by extending resolving sets to different subjects in graph
theory, such as the partition of the vertex set, decomposition
and coloring in graphs, or by combining resolving property with
another graph-theoretic property such as being connected,
independent, or acyclic. In this paper, we survey results and
open questions on the resolving parameters defined by imposing an
additional constraint on resolving sets, resolving partitions, or
resolving decompositions in graphs. |
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| ISSN: | 0161-1712 1687-0425 |