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On the (M,D) number of a graph.

Author
John, J.

Sudhahar, P. Arul Paul

Stalin, D.

Full text
http://www.revistaproyecciones.cl/article/view/3570
Abstract
For a connected graph G = (V, E), a monophonic set of G is a set M ⊆ V (G) such that every vertex of G is contained in a monophonic path joining some pair of vertices in M. A subset D of vertices in G is called dominating set if every vertex not in D has at least one neighbour in D. A monophonic dominating set M is both a monophonic and a dominating set. The monophonic, dominating, monophonic domination number m(G), γ(G), γm(G) respectively are the minimum cardinality of the respective sets in G. Monophonic domination number of certain classes of graphs are determined. Connected graph of order p with monophonic domination number p− 1 or p is characterised. It is shown that for every two intigers a, b ≥ 2 with 2 ≤ a ≤ b, there is a connected graph G such that γm(G) = a and γg(G) = b, where γg(G) is the geodetic domination number of a graph.
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Artes, Arquitectura y UrbanismoCiencias Agrarias, Forestales y VeterinariasCiencias Exactas y NaturalesCiencias SocialesDerechoEconomía y AdministraciónFilosofía y HumanidadesIngenieríaMedicinaMultidisciplinarias
Institutions
Universidad de ChileUniversidad Católica de ChileUniversidad de Santiago de ChileUniversidad de ConcepciónUniversidad Austral de ChileUniversidad Católica de ValparaísoUniversidad del Bio BioUniversidad de ValparaísoUniversidad Católica del Nortemore

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