Maximal resolving sets in a graph
Let G be a connected graph. A subset [Formula: see text] of [Formula: see text] is called a resolving set of G if the code of any vertex [Formula: see text] with respect to S is different from the code of any other vertex where code of u with respect to S denoted by [Formula: see text] is defined as...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
World Scientific Publishing
2024-12-01
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| Series: | International Journal of Mathematics for Industry |
| Subjects: | |
| Online Access: | https://www.worldscientific.com/doi/10.1142/S2661335224500059 |
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| Summary: | Let G be a connected graph. A subset [Formula: see text] of [Formula: see text] is called a resolving set of G if the code of any vertex [Formula: see text] with respect to S is different from the code of any other vertex where code of u with respect to S denoted by [Formula: see text] is defined as [Formula: see text]. Resolving set was earlier studied in the name of locating set by Slater and Harary and Melter too studied this concept. The minimum cardinality of a resolving set is called the metric dimension (locating number). A vertex [Formula: see text] in a connected graph G is said to resolve two vertices [Formula: see text] if [Formula: see text] Clearly, x resolves [Formula: see text] A subset S of [Formula: see text] is a resolving set of G if for any two distinct vertices [Formula: see text] there exists a vertex [Formula: see text] such that x resolves [Formula: see text] Motivated by this equivalent definition, a study of resolving chain and maximal resolving set is initiated in this paper. Also, study of total resolving sets is initiated. |
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| ISSN: | 2661-3352 2661-3344 |