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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
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
|
| Series: | Ural Mathematical Journal |
| Online Access: | https://umjuran.ru/index.php/umj/article/view/174 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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 \(G\). |
|---|---|
| ISSN: | 2414-3952 |