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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.32 no.2 Antofagasta May 2013

http://dx.doi.org/10.4067/S0716-09172013000200007 

Proyecciones Journal of Mathematics Vol. 32, No 2, pp. 183-198, June 2013. Universidad Católica del Norte Antofagasta - Chile

Edge Detour Monophonic Number of a Graph

A. P. Santhakumaran

Hindustan University, India

P. Titus K. Ganesamoorthy

P. Balakrishnan

University College of Engineering Nagercoil, India


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 ≤ 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.

Key Words : monophonic number, edge monophonic number, detour monophonic number, edge detour monophonic number.

AMS Subject Classification : 05C12.


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A. P. Santhakumaran
Department of Mathematics Hindustan University
Hindustan Institute of Technology and Science
Chennai - 603 103, India
e-mail: apskumar1953@yahoo.co.in

P. Titus
e-mail : titusvino@yahoo.com

K. Ganesamoorthy
e-mail : kvgm_2005@yahoo.co.in

P. Balakrishnan
Department of Mathematics
University College of Engineering Nagercoil
Anna University,
Tirunelveli Region
Nagercoil - 629 004,
India
e-mail : gangaibala1@yahoo.com

Received : December 2012. Accepted : April 2013

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