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

• John, J. ^[3] ; Sudhahar, P. Arul Paul ^[1] ; Stalin, D. ^[2]
  1. [1] Government College for Women Anantnag

     Government College for Women Anantnag

     India

     
  2. [2] Bharathiar University

     Bharathiar University

     India

     
  3. [3] Government College of Engineering, Tirunelveli.

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• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 38, Nº. 2, 2019, págs. 255-266
• Idioma: inglés
• DOI: 10.4067/s0716-09172019000200255
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• Resumen

  • 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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