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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.35 no.1 Antofagasta Mar. 2016

http://dx.doi.org/10.4067/S0716-09172016000100005 

Proyecciones Journal of Mathematics Vol. 35, No 1, pp. 67-83, March 2016. Universidad Católica del Norte Antofagasta - Chile

The forcing open monophonic number of a graph

A. P. Santhakumaran

M. Mahendran

Hindustan University

India 


ABSTRACT

For a connected graph G of order n ≥ 2, and for any mínimum open monophonic set S of G, a subset T of S is called a forcing subset for S if S is the unique minimum open monophonic set containing T. A forcing subset for S of minimum cardinality is a minimum forcing subset of S. The forcing open monophonic number of S, de-noted by fom(S), is the cardinality of a minimum forcing subset of S. The forcing open monophonic number of G, denoted by fom(G), is fom(G) = min(fom(S)), where the minimum is taken over all minimum open monophonic sets in G. The forcing open monophonic numbers of certain standard graphs are determined. It is proved that for every pair a, b of integers with 0 ≤ a ≤ b — 4 and b ≥ 5, there exists a connected graph G such that fom(G) = a and om(G) = b. It is analyzed how the addition of a pendant edge to certain standard graphs affects the forcing open monophonic number.

2010 Mathematics Subject Classification : 05C12, 05C70.

Key Words : Monophonic number, open monophonic number, forcing monophonic number, forcing open monophonic number.


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[9]    A. P. Santhakumaran and M. Mahendran, The connected open mono-phonic number of a graph, International Journal of Computer Applications (0975-8887), Vol. 80 No. 1, pp. 39-42, (2013).         [ Links ]

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[12]    A. P. Santhakumaran and M. Mahendran, The upper open mono-phonic number of a graph, Proyecciones Journal of Mathematics, Vol. 33 No. 4, pp. 389-403, (2014).         [ Links ]

A. P. Santhakumaran

Department of Mathematics Hindustan University

Hindustan Institute of Technology and Science Chennai-603 103,

India

e-mail : apskumar1953@gmail.com

M. Mahendran

Department of Mathematics Hindustan University

Hindustan Institute of Technology and Science Chennai-603 103,

India

e-mail : magimani83@gmail.com

Received : April 2015. Accepted : March 2016

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