Discussiones Mathematicae Graph Theory 32(2) (2012)
191-204

doi: 10.7151/dmgt.1599

A.P. Santhakumaran
Department of Mathematics | P.Titus
Department of Mathematics |

**Keywords:** monophonic path, monophonic number, vertex monophonic number

**2010 Mathematics Subject Classification:** 05C12.

[1] | F. Buckley and F. Harary, Distance in Graphs (Addison-Wesley, Redwood City, CA, 1990). |

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[5] | G. Chartrand, G.L. Johns and P. Zhang, On the detour number and geodetic number of a graph, Ars Combinatoria 72 (2004) 3--15. |

[6] | F. Harary, Graph Theory (Addison-Wesley, 1969). |

[7] | F. Harary, E. Loukakis and C. Tsouros, The geodetic number of a graph, Math. Comput. Modeling 17(11) (1993) 87--95, doi: 10.1016/0895-7177(93)90259-2. |

[8] | A.P. Santhakumaran and P. Titus, Vertex geodomination in graphs, Bulletin of Kerala Mathematics Association, 2(2) (2005) 45--57. |

[9] | A.P. Santhakumaran and P. Titus, On the vertex geodomination number of a graph, Ars Combinatoria, to appear. |

[10] | A.P. Santhakumaran, P. Titus, The vertex detour number of a graph, AKCE International J. Graphs. Combin. 4(1) (2007) 99--112. |

[11] | A.P. Santhakumaran and P. Titus, Monophonic distance in graphs, Discrete Mathematics, Algorithms and Applications, to appear. |

Received 10 June 2010

Revised 11 February 2011

Accepted 14 February 2011