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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.40 no.2 Antofagasta Apr. 2021

http://dx.doi.org/10.22199/issn.0717-6279-2021-02-0031 

Artículos

The forcing total monophonic number of a graph

1Hindustan Institute of Technology and Science. Dept. of Mathematics, Chennai, TN, India. E-mail: apskumar1953@gmail.com

2University College of Engineering Nagercoil, Dept. of Mathematics, Nagercoil, TN, India. E-mail: titusvino@yahoo.com

3Coimbatore Institute of Technology, Dept. of Mathematics, Coimbatore , TN, India. E-mail: kvgm_2005@yahoo.co.in

4Coimbatore Institute of Technology, Dept. of Mathematics, Coimbatore , TN, India. E-mail: jrfmaths@gmail.com

Abstract

For a connected graph G = (V, E) of order at least two, a subset T of a minimum total monophonic set S of G is a forcing total monophonic subset for S if S is the unique minimum total monophonic set containing T . A forcing total monophonic subset for S of minimum cardinality is a minimum forcing total monophonic subset of S. The forcing total monophonic number f tm (S) in G is the cardinality of a minimum forcing total monophonic subset of S. The forcing total monophonic number of G is f tm (G) = min{f tm (S)}, where the minimum is taken over all minimum total monophonic sets S in G. We determine bounds for it and find the forcing total monophonic number of certain classes of graphs. It is shown that for every pair a, b of positive integers with 0 ≤ a < b and b ≥ a+4, there exists a connected graph G such that f tm (G) = a and m t (G) = b.

Keywords: Total monophonic set; Total monophonic number; Forcing total monophonic subset; Forcing total monophonic number

Texto completo disponible sólo en PDF

Full text available only in PDF format.

Acknowledgements

The third author acknowledges support from Research supported by NBHM Project No. NBHM/R.P.29/2015/Fresh/157.

References

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Received: April 30, 2019; Accepted: January 31, 2021

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