The forcing open monophonic number of a graph

• Santhakumaran, A. P. ^[1] ; Mahendran, M. ^[1]
  1. [1] Hindustan University

     Hindustan University

     India

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 35, Nº. 1, 2016, págs. 67-83
• Idioma: inglés
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• Resumen

  • 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.