The forcing total monophonic number of a graph

Authors

DOI:

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

Keywords:

Total monophonic set, Total monophonic number, Forcing total monophonic subset, Forcing total monophonic number

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 ftm(S) in G is the cardinality of a minimum forcing total monophonic subset of S. The forcing total monophonic number of G is ftm(G) = min{ftm(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 ftm(G) = a and mt(G) = b.

Author Biographies

A. P. Santhakumaran, Hindustan Institute of Technology and Science.

Dept. of Mathematics

P. Titus, University College of Engineering Nagercoil

Dept. of Mathematics

K. Ganesamoorthy, Coimbatore Institute of Technology

Dept. of Mathematics

M. Murugan, Coimbatore Institute of Technology

Dept. of Mathematics

References

F. Buckley and F. Harary, Distance in graphs. Redwood City, CA: Addison-Wesley, 1990.

F. Harary, Graph theory. Reading, MA: Addison-Wesley, 1969. [On line]. Available: https://bit.ly/38wIHRk

K. Ganesamoorthy, "A study of monophonic number and its variants", Ph.D. thesis, Anna University, Chennai, 2013.

E. M. Paluga and S. R. Canoy, “Monophonic numbers of the join and composition of connected graphs”, Discrete mathematics, vol. 307, no. 9-10, pp. 1146-1154, 2007, doi: 10.1016/j.disc.2006.08.002

A. P. Santhakumaran, P. Titus and K. Ganesamoorthy, “On the monophonic number of a graph”, Journal of applied mathematics & informatics, vol. 32, no. 1-2, pp. 255-266, 2014, doi: 10.14317/jami.2014.255

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.

Published

2021-03-15

How to Cite

[1]
A. P. . Santhakumaran, P. . Titus, K. Ganesamoorthy, and M. . Murugan, “The forcing total monophonic number of a graph”, Proyecciones (Antofagasta, On line), vol. 40, no. 2, pp. 561-571, Mar. 2021.

Issue

Vol. 40 No. 2 (2021)

Section

Artículos

Copyright (c) 2021 A. P. Santhakumaran, P. Titus, K. Ganesamoorthy, M. Murugan

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