RESTRAINED DOUBLE MONOPHONIC NUMBER OF A GRAPH
For a connected graph \(G\) of order at least two, a double monophonic set \(S\) of a graph \(G\) is a restrained double monophonic set if either \(S=V\) or the subgraph induced by \(V-S\) has no isolated vertices. The minimum cardinality of a restrained double monophonic set of \(G\) is the restr...
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| Language: | English |
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Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
2019-12-01
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| Series: | Ural Mathematical Journal |
| Online Access: | https://umjuran.ru/index.php/umj/article/view/174 |
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| author | A.P. Santhakumaran K. Ganesamoorthy |
| author_facet | A.P. Santhakumaran K. Ganesamoorthy |
| author_sort | A.P. Santhakumaran |
| collection | DOAJ |
| description | For a connected graph \(G\) of order at least two, a double monophonic set \(S\) of a graph \(G\) is a restrained double monophonic set if either \(S=V\) or the subgraph induced by \(V-S\) has no isolated vertices. The minimum cardinality of a restrained double monophonic set of \(G\) is the restrained double monophonic number of \(G\) and is denoted by \(dm_{r}(G)\). The restrained double monophonic number of certain classes graphs are determined. It is shown that for any integers \(a,\, b,\, c\) with \(3 \leq a \leq b \leq c\), there is a connected graph \(G\) with \(m(G) = a\), \(m_r(G) = b\) and \(dm_{r}(G) = c\), where \(m(G)\) is the monophonic number and \(m_r(G)\) is the restrained monophonic number of a graph \(G\). |
| format | Article |
| id | doaj-art-2bfb5509500644dcb7abe085acedda51 |
| institution | Kabale University |
| issn | 2414-3952 |
| language | English |
| publishDate | 2019-12-01 |
| publisher | Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj-art-2bfb5509500644dcb7abe085acedda512025-08-20T03:29:32ZengUral Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and MechanicsUral Mathematical Journal2414-39522019-12-015210.15826/umj.2019.2.00587RESTRAINED DOUBLE MONOPHONIC NUMBER OF A GRAPHA.P. Santhakumaran0K. Ganesamoorthy1Department of Mathematics, Hindustan Institute of Technology and Science, Chennai - 603 103Department of Mathematics, Coimbatore Institute of Technology, Coimbatore - 641 014For a connected graph \(G\) of order at least two, a double monophonic set \(S\) of a graph \(G\) is a restrained double monophonic set if either \(S=V\) or the subgraph induced by \(V-S\) has no isolated vertices. The minimum cardinality of a restrained double monophonic set of \(G\) is the restrained double monophonic number of \(G\) and is denoted by \(dm_{r}(G)\). The restrained double monophonic number of certain classes graphs are determined. It is shown that for any integers \(a,\, b,\, c\) with \(3 \leq a \leq b \leq c\), there is a connected graph \(G\) with \(m(G) = a\), \(m_r(G) = b\) and \(dm_{r}(G) = c\), where \(m(G)\) is the monophonic number and \(m_r(G)\) is the restrained monophonic number of a graph \(G\).https://umjuran.ru/index.php/umj/article/view/174 |
| spellingShingle | A.P. Santhakumaran K. Ganesamoorthy RESTRAINED DOUBLE MONOPHONIC NUMBER OF A GRAPH Ural Mathematical Journal |
| title | RESTRAINED DOUBLE MONOPHONIC NUMBER OF A GRAPH |
| title_full | RESTRAINED DOUBLE MONOPHONIC NUMBER OF A GRAPH |
| title_fullStr | RESTRAINED DOUBLE MONOPHONIC NUMBER OF A GRAPH |
| title_full_unstemmed | RESTRAINED DOUBLE MONOPHONIC NUMBER OF A GRAPH |
| title_short | RESTRAINED DOUBLE MONOPHONIC NUMBER OF A GRAPH |
| title_sort | restrained double monophonic number of a graph |
| url | https://umjuran.ru/index.php/umj/article/view/174 |
| work_keys_str_mv | AT apsanthakumaran restraineddoublemonophonicnumberofagraph AT kganesamoorthy restraineddoublemonophonicnumberofagraph |