Edge fixed monophonic number of a graph.

Authors

  • P. Titus University College of Engineering Nagercoil.
  • S. Eldin Vanaja University College of Engineering.

Keywords:

Monophonic path, Vertex monophonic number, Edge fixed monophonic number

Abstract

For an edge xy in a connected graph G of order p ≥ 3, a set SCV(G)is an xy-monophonic set of G if each vertex v Є V(G) lies on an x-u monophonic path or a y-u monophonic path for some element u in S. The minimum cardinality of an xy- monophonic set of G is defined as the xy-monophonic number of G, denoted by mxy (G). An xy-monophonic set of cardinality mxy (G) is called a mxy -set of G. We determine bounds for it and find the same for special classes of graphs. It is shown that for any three positive integers r, d and n ≥ 2 with 2 ≤ r ≤ d, there exists a connected graph G with monophonic radius r, monophonic diameter d and mxy (G) = n for some edge xy in G.

Author Biographies

P. Titus, University College of Engineering Nagercoil.

Department of Mathematics.

S. Eldin Vanaja, University College of Engineering.

Department of Mathematics.

References

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

F. Harary, Graph Theory, Addison-Wesley, Reading Mass, (1969).

A. P. Santhakumaran and P. Titus, Monophonic distance in graphs, Discrete Mathematics, Algorithms and Applications, Vol. 3, No. 2, pp. 159-169, (2011).

A. P. Santhakumaran and P. Titus, A note on ‘Monophonic distance in graphs’, Discrete Mathematics, Algorithms and Applications, Vol. 4, No. 2 (2012), DOI: 10.1142/S1793830912500188.

A. P. Santhakumaran and P. Titus, The vertex monophonic number of a graph, Discussiones Mathematicae Graph Theory, 32, pp. 189-202, (2012).

Published

2017-10-20

How to Cite

[1]
P. Titus and S. Eldin Vanaja, “Edge fixed monophonic number of a graph.”, Proyecciones (Antofagasta, On line), vol. 36, no. 3, pp. 363-372, Oct. 2017.

Issue

Section

Artículos