Characterization of Upper Detour Monophonic Domination Number
Abstract 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 ⊆ V (G) is called minimal detour monophonic dominating set, if no proper subset of M is a detour monophonic dominating set. The maximum...
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| Autor principal: | |
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| Lenguaje: | English |
| Publicado: |
Universidad de La Frontera. Departamento de Matemática y Estadística.
2020
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462020000300315 |
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| Sumario: | Abstract 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 ⊆ 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 γ+ dm (G). For any two positive integers p and q with 2 ≤ p ≤ q there is a connected graph G with γm (G) = γdm (G) = p and γ+ 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, γdm (G) = q and γ+ dm (G) = r. Let p and q be two positive integers with 2 < p < q such that γdm (G) = p and γ+ 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 ≤ p ≤ q ≤ r. Then, there exist a connected graph G such that γm (G)= p, γ+ dm (G) = q and |V (G)| = r. |
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