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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Abstract

SANTHAKUMARAN, A. P.; TITUS, P.; GANESAMOORTHY, K.  and  MURUGAN, M.. The forcing total monophonic number of a graph. Proyecciones (Antofagasta) [online]. 2021, vol.40, n.2, pp.561-571. ISSN 0716-0917.  http://dx.doi.org/10.22199/issn.0717-6279-2021-02-0031.

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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