On the (M, D) number of a graph
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...
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Universidad Católica del Norte, Departamento de Matemáticas
2019
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oai:scielo:S0716-091720190002002552019-05-30On the (M, D) number of a graphJohn,J.Paul Sudhahar,P. ArulStalin,D. monophonic number domination number monophonic domination number geodetic domination number 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.38 n.2 20192019-06-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000200255en10.4067/S0716-09172019000200255 |
| institution |
Scielo Chile |
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Scielo Chile |
| language |
English |
| topic |
monophonic number domination number monophonic domination number geodetic domination number |
| spellingShingle |
monophonic number domination number monophonic domination number geodetic domination number John,J. Paul Sudhahar,P. Arul Stalin,D. On the (M, D) number of a graph |
| description |
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. |
| author |
John,J. Paul Sudhahar,P. Arul Stalin,D. |
| author_facet |
John,J. Paul Sudhahar,P. Arul Stalin,D. |
| author_sort |
John,J. |
| title |
On the (M, D) number of a graph |
| title_short |
On the (M, D) number of a graph |
| title_full |
On the (M, D) number of a graph |
| title_fullStr |
On the (M, D) number of a graph |
| title_full_unstemmed |
On the (M, D) number of a graph |
| title_sort |
on the (m, d) number of a graph |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2019 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000200255 |
| work_keys_str_mv |
AT johnj onthemdnumberofagraph AT paulsudhaharparul onthemdnumberofagraph AT stalind onthemdnumberofagraph |
| _version_ |
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