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
• DOI: 10.4067/S0716-09172016000100005
• Enlaces
  • Texto completo
• 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.

• Referencias bibliográficas
  • Citas [1] F. Buckley and F. Harary, Distance in graphs, Addison-Wesley, Redwood city, CA, (1990).
  • [2] G. Chartrand, F. Harary, H. C. Swart and P. Zhang, Geodomination in graphs, Bulletin of the ICA, 31, pp. 51-59, (2001).
  • [3] G. Chartrand, E. M. Palmer and P. Zhang, The geodetic number of a graph: A survey, Congr. Numer., 156, pp. 37-58, (2002).
  • [4] W. Hale, Frequency Assignment; Theory and Applications, Proc. IEEE 68, pp. 1497-1514, (1980).
  • [5] F. Harary, Graph Theory, Addison-Wesley, (1969).
  • [6] R. Muntean and P. Zhang, On geodomination in graphs, Congr. Numer., 143, pp. 161-174, (2000).
  • [7] P. A. Ostrand, Graphs with specified radius and diameter, Discrete Math., 4, pp. 71-75, (1973).
  • [8] A. P. Santhakumaran and T. Kumari Latha, On the open geodetic number of a graph, SCIENTIA Series A: Mathematical Sciences, Vol. 20, pp....
  • [9] A. P. Santhakumaran and M. Mahendran, The connected open monophonic number of a graph, International Journal of Computer Applications...
  • [10] A. P. Santhakumaran and M. Mahendran, The open monophonic number of a graph, International Journal of Scientific & Engineering Research,...
  • [11] A. P. Santhakumaran and M. Mahendran, The total open monophonic number of a graph, Journal of Advances in Mathematics, Vol. 9 No. 3,...
  • [12] A. P. Santhakumaran and M. Mahendran, The upper open monophonic number of a graph, Proyecciones Journal of Mathematics, Vol. 33 No. 4,...