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

• J. John Government College of Engineering, Tirunelveli.
• P. Arul Paul Sudhahar Rani Anna Government College for Women. https://orcid.org/0000-0002-5313-0357
• D. Stalin Bharathiar University.

### 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.

### Biografía del autor

J. John, Government College of Engineering, Tirunelveli.
Department of Mathematics.
P. Arul Paul Sudhahar, Rani Anna Government College for Women.
Department of Mathematics.
D. Stalin, Bharathiar University.
Research and Development Center.

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