| dc.creator | Abdul Khayyoom, M. Mohammed | |
| dc.date | 2020-12-07 | |
| dc.date.accessioned | 2021-08-17T20:35:26Z | |
| dc.date.available | 2021-08-17T20:35:26Z | |
| dc.identifier | http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2467 | |
| dc.identifier | 10.4067/S0719-06462020000300315 | |
| dc.identifier.uri | https://revistaschilenas.uchile.cl/handle/2250/174236 | |
| dc.description | This paper introduces the concept of upper detour monophonic domination number of a graph. For a connected graph \( G \) with vertex set \( V(G) \), a set \( M\subseteq V(G) \) is called minimal detour monophonic dominating set, if no proper subset of \( M \) is a detour monophonic dominating set. The maximum cardinality among all minimal monophonic dominating sets is called upper detour monophonic domination number and is denoted by \( \gamma_{dm}^+(G) \). For any two positive integers \( p \) and \( q \) with \( 2 \leq p \leq q \) there is a connected graph \( G \) with \( \gamma_m (G) = \gamma_{dm}(G) = p \) and \( \gamma_{dm}^+(G)=q \). For any three positive integers \( p, q, r \) with \(2 < p < q < r\), there is a connected graph \( G \) with \( m(G) = p \), \( \gamma_{dm}(G) = q \) and \( \gamma_{dm}^+(G)= r \). Let \( p \) and \( q \) be two positive integers with \( 2 < p<q \) such that \( \gamma_{dm}(G) = p \) and \( \gamma_{dm}^+(G)= q \). Then there is a minimal DMD set whose cardinality lies between \( p \) and \( q \). Let \( p , q \) and \( r \) be any three positive integers with \( 2 \leq p \leq q \leq r\). Then, there exist a connected graph \( G \) such that \( \gamma_{dm}(G) = p , \gamma_{dm}^+(G)= q \) and \( \lvert V(G) \rvert = r\). | en-US |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Universidad de La Frontera. Temuco, Chile. | en-US |
| dc.relation | http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2467/2024 | |
| dc.rights | https://creativecommons.org/licenses/by-nc/4.0/ | en-US |
| dc.source | CUBO, A Mathematical Journal; Vol. 22 No. 3 (2020); 315–324 | en-US |
| dc.source | CUBO, A Mathematical Journal; Vol. 22 Núm. 3 (2020); 315–324 | es-ES |
| dc.source | 0719-0646 | |
| dc.source | 0716-7776 | |
| dc.subject | Monophonic number | en-US |
| dc.subject | Domination Number | en-US |
| dc.subject | Detour monophonic number | en-US |
| dc.subject | Detour monophonic domination number | en-US |
| dc.subject | Upper detour monophonic domination number | en-US |
| dc.title | Characterization of Upper Detour Monophonic Domination Number | en-US |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
