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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World Scientific Publishing
2024-12-01
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| Series: | International Journal of Mathematics for Industry |
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| Online Access: | https://www.worldscientific.com/doi/10.1142/S2661335224500059 |
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| author | V. Swaminathan R. Sundareswaran |
| author_facet | V. Swaminathan R. Sundareswaran |
| author_sort | V. Swaminathan |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-7bf8e5e3b89548e2929d5161b8f6fd6b |
| institution | Kabale University |
| issn | 2661-3352 2661-3344 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | World Scientific Publishing |
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| series | International Journal of Mathematics for Industry |
| spelling | doaj-art-7bf8e5e3b89548e2929d5161b8f6fd6b2025-01-31T06:15:28ZengWorld Scientific PublishingInternational Journal of Mathematics for Industry2661-33522661-33442024-12-01160110.1142/S2661335224500059Maximal resolving sets in a graphV. Swaminathan0R. Sundareswaran1Ramanujan Research Center in Mathematics, Saraswathi Narayanan College, Madurai 625022, IndiaDepartment of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Chennai 603110, IndiaLet 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.https://www.worldscientific.com/doi/10.1142/S2661335224500059Resolving setmetric dimensionmaximal resolving set |
| spellingShingle | V. Swaminathan R. Sundareswaran Maximal resolving sets in a graph International Journal of Mathematics for Industry Resolving set metric dimension maximal resolving set |
| title | Maximal resolving sets in a graph |
| title_full | Maximal resolving sets in a graph |
| title_fullStr | Maximal resolving sets in a graph |
| title_full_unstemmed | Maximal resolving sets in a graph |
| title_short | Maximal resolving sets in a graph |
| title_sort | maximal resolving sets in a graph |
| topic | Resolving set metric dimension maximal resolving set |
| url | https://www.worldscientific.com/doi/10.1142/S2661335224500059 |
| work_keys_str_mv | AT vswaminathan maximalresolvingsetsinagraph AT rsundareswaran maximalresolvingsetsinagraph |