The forcing total monophonic number of a graph

Santhakumaran, A. P.; Titus, P.; Ganesamoorthy, K.; Murugan, M.; Santhakumaran, A. P.; Titus, P.; Ganesamoorthy, K.; Murugan, M.

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

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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

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

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

Artículos

The forcing total monophonic number of a graph

A. P. Santhakumaran¹
http://orcid.org/0000-0002-8639-1246

P. Titus²
http://orcid.org/0000-0001-5724-0935

K. Ganesamoorthy³
http://orcid.org/0000-0003-2769-1991

M. Murugan⁴
http://orcid.org/0000-0002-0281-3692

^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

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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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[6] A. P. Santhakumaran , P. Titus, K. Ganesamoorthy, and M. Murugan, “The Total Monophonic Number of a Graph”, in Proceedings of International Conference on Discrete Mathematics and its Applications to Network Science (ICDMANS 2018), Under process. [ Links ]

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

Article copyright: © 2021 A. P. Santhakumaran, P. Titus, K. Ganesamoorthy and M. Murugan. This is an open access article distributed under the terms of the Creative Commons License, which permits unrestricted use and distribution provided the original author and source are credited

This is an open-access article distributed under the terms of the Creative Commons Attribution License