ON DOUBLE SIGNAL NUMBER OF A GRAPH
A set \(S\) of vertices in a connected graph \(G=(V,E)\) is called a signal set if every vertex not in \(S\) lies on a signal path between two vertices from \(S\). A set \(S\) is called a double signal set of \(G\) if \(S\) if for each pair of vertices \(x,y \in G\) there exist \(u,v \in S\) such th...
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| Format: | Article |
| Language: | English |
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Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.
2022-07-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/383 |
| _version_ | 1818018779738669056 |
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| author | X. Lenin Xaviour S. Ancy Mary |
| author_facet | X. Lenin Xaviour S. Ancy Mary |
| author_sort | X. Lenin Xaviour |
| collection | DOAJ |
| description | A set \(S\) of vertices in a connected graph \(G=(V,E)\) is called a signal set if every vertex not in \(S\) lies on a signal path between two vertices from \(S\). A set \(S\) is called a double signal set of \(G\) if \(S\) if for each pair of vertices \(x,y \in G\) there exist \(u,v \in S\) such that \(x,y \in L[u,v]\). The double signal number \(\mathrm{dsn}\,(G)\) of \(G\) is the minimum cardinality of a double signal set. Any double signal set of cardinality \(\mathrm{dsn}\,(G)\) is called \(\mathrm{dsn}\)-set of \(G\). In this paper we introduce and initiate some properties on double signal number of a graph. We have also given relation between geodetic number, signal number and double signal number for some classes of graphs. |
| first_indexed | 2024-04-14T07:44:21Z |
| format | Article |
| id | doaj.art-86d661700d394360a54b73f7dbe85ae5 |
| institution | Directory Open Access Journal |
| issn | 2414-3952 |
| language | English |
| last_indexed | 2024-04-14T07:44:21Z |
| publishDate | 2022-07-01 |
| publisher | Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin. |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj.art-86d661700d394360a54b73f7dbe85ae52022-12-22T02:05:24ZengKrasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.Ural Mathematical Journal2414-39522022-07-018110.15826/umj.2022.1.007142ON DOUBLE SIGNAL NUMBER OF A GRAPHX. Lenin Xaviour0S. Ancy Mary1Department of Mathematics, Nesamony Memorial Christian College, Marthandam – 629165, Tamil NaduDepartment of Mathematics, St. John’s College of Arts and Science, Ammandivilai, Affliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli – 627012, Tamil NaduA set \(S\) of vertices in a connected graph \(G=(V,E)\) is called a signal set if every vertex not in \(S\) lies on a signal path between two vertices from \(S\). A set \(S\) is called a double signal set of \(G\) if \(S\) if for each pair of vertices \(x,y \in G\) there exist \(u,v \in S\) such that \(x,y \in L[u,v]\). The double signal number \(\mathrm{dsn}\,(G)\) of \(G\) is the minimum cardinality of a double signal set. Any double signal set of cardinality \(\mathrm{dsn}\,(G)\) is called \(\mathrm{dsn}\)-set of \(G\). In this paper we introduce and initiate some properties on double signal number of a graph. We have also given relation between geodetic number, signal number and double signal number for some classes of graphs.https://umjuran.ru/index.php/umj/article/view/383signal set, geodetic set, double signal set, double signal number. |
| spellingShingle | X. Lenin Xaviour S. Ancy Mary ON DOUBLE SIGNAL NUMBER OF A GRAPH Ural Mathematical Journal signal set, geodetic set, double signal set, double signal number. |
| title | ON DOUBLE SIGNAL NUMBER OF A GRAPH |
| title_full | ON DOUBLE SIGNAL NUMBER OF A GRAPH |
| title_fullStr | ON DOUBLE SIGNAL NUMBER OF A GRAPH |
| title_full_unstemmed | ON DOUBLE SIGNAL NUMBER OF A GRAPH |
| title_short | ON DOUBLE SIGNAL NUMBER OF A GRAPH |
| title_sort | on double signal number of a graph |
| topic | signal set, geodetic set, double signal set, double signal number. |
| url | https://umjuran.ru/index.php/umj/article/view/383 |
| work_keys_str_mv | AT xleninxaviour ondoublesignalnumberofagraph AT sancymary ondoublesignalnumberofagraph |