On the Distance Pattern Distinguishing Number of a Graph
Let G=(V,E) be a connected simple graph and let M be a nonempty subset of V. The M-distance pattern of a vertex u in G is the set of all distances from u to the vertices in M. If the distance patterns of all vertices in V are distinct, then the set M is a distance pattern distinguishing set of G. A...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/328703 |
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| author | Sona Jose Germina K. Augustine |
| author_facet | Sona Jose Germina K. Augustine |
| author_sort | Sona Jose |
| collection | DOAJ |
| description | Let G=(V,E) be a connected simple graph and let M be a nonempty subset of V. The M-distance pattern of a vertex u in G is the set of all distances from u to the vertices in M. If the distance patterns of all vertices in V are distinct, then the set M is a distance pattern distinguishing set of G. A graph G with a distance pattern distinguishing set is called a distance pattern distinguishing graph. Minimum number of vertices in a distance pattern distinguishing set is called distance pattern distinguishing number of a graph. This paper initiates a study on the problem of finding distance pattern distinguishing number of a graph and gives bounds for distance pattern distinguishing number. Further, this paper provides an algorithm to determine whether a graph is a distance pattern distinguishing graph or not and hence to determine the distance pattern distinguishing number of that graph. |
| format | Article |
| id | doaj-art-7975fd51742345a292682604f53c691d |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-7975fd51742345a292682604f53c691d2025-02-03T01:04:18ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/328703328703On the Distance Pattern Distinguishing Number of a GraphSona Jose0Germina K. Augustine1Centre for Mathematical Sciences, Pala Campus, Arunapuram, Kerala 686 574, IndiaCentre for Mathematical Sciences, Pala Campus, Arunapuram, Kerala 686 574, IndiaLet G=(V,E) be a connected simple graph and let M be a nonempty subset of V. The M-distance pattern of a vertex u in G is the set of all distances from u to the vertices in M. If the distance patterns of all vertices in V are distinct, then the set M is a distance pattern distinguishing set of G. A graph G with a distance pattern distinguishing set is called a distance pattern distinguishing graph. Minimum number of vertices in a distance pattern distinguishing set is called distance pattern distinguishing number of a graph. This paper initiates a study on the problem of finding distance pattern distinguishing number of a graph and gives bounds for distance pattern distinguishing number. Further, this paper provides an algorithm to determine whether a graph is a distance pattern distinguishing graph or not and hence to determine the distance pattern distinguishing number of that graph.http://dx.doi.org/10.1155/2014/328703 |
| spellingShingle | Sona Jose Germina K. Augustine On the Distance Pattern Distinguishing Number of a Graph Journal of Applied Mathematics |
| title | On the Distance Pattern Distinguishing Number of a Graph |
| title_full | On the Distance Pattern Distinguishing Number of a Graph |
| title_fullStr | On the Distance Pattern Distinguishing Number of a Graph |
| title_full_unstemmed | On the Distance Pattern Distinguishing Number of a Graph |
| title_short | On the Distance Pattern Distinguishing Number of a Graph |
| title_sort | on the distance pattern distinguishing number of a graph |
| url | http://dx.doi.org/10.1155/2014/328703 |
| work_keys_str_mv | AT sonajose onthedistancepatterndistinguishingnumberofagraph AT germinakaugustine onthedistancepatterndistinguishingnumberofagraph |