Edge Detour Monophonic Number of a Graph

Authors

  • A. P. Santhakumaran Hindustan University.
  • P. Titus University College of Engineering Nagercoil.
  • K. Ganesamoorthy Anna University.
  • P. Balakrishnan University College of Engineering Nagercoil.

DOI:

https://doi.org/10.4067/S0716-09172013000200007

Keywords:

Monophonic number, Edge monophonic number, Detour monophonic number, Edge detour monophonic number.

Abstract

For a connected graph G of order at least two, an edge detour monophonic set of G is a set S of vertices such that every edge of G lies on a detour monophonic path joining some pair of vertices in S. The edge detour monophonic number of G is the minimum cardinality of its edge detour monophonic sets and is denoted by edm(G) .We determine bounds for it and characterize graphs which realize these bounds. Also, certain general properties satisfied by an edge detour monophonic set are studied. It is shown that for positive integers a, b and c with 2 < a < b < c, there exists a connected graph G such that m(G) = a, m!(G) = b and edm(G) = c,where m(G) is the monophonic number and m! (G) is the edge monophonic number of G. Also, for any integers a and b with 2 < a < b, there exists a connected graph G such that dm(G) = a and edm(G)= b,where dm(G) is the detour monophonic number of a graph G.

References

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[10] P. Titus and K. Ganesamoorthy, On the Detour Monophonic Number of a Graph, Ars Combinatoria, to appear.

Published

2013-06-24

How to Cite

[1]
A. P. Santhakumaran, P. Titus, K. Ganesamoorthy, and P. Balakrishnan, “Edge Detour Monophonic Number of a Graph”, Proyecciones (Antofagasta, On line), vol. 32, no. 2, pp. 183-198, Jun. 2013.

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