Minimal connected restrained monophonic sets in graphs

• Santhakumaran, A. P. ^[1] ; Titus, P. ^[2] ; Ganesamoorthy, K. ^[3]
  1. [1] Hindustan Institute of Technology and Science.
  2. [2] University College of Engineering Nagercoil.
  3. [3] Coimbatore Institute of Technology.

  Mostrar afiliaciones +
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 41, Nº. 4, 2022, págs. 879-890
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-4475
• Enlaces
  • Texto completo
• Resumen

  • For a connected graph G = (V,E) of order at least two, a connected restrained monophonic set S of G is a restrained monophonic set such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected restrained monophonic set of G is the connected restrained monophonic number of G and is denoted by mcr(G). A connected restrained monophonic set S of G is called a minimal connected restrained monophonic set if no proper subset of S is a connected restrained monophonic set of G. The upper connected restrained monophonic number of G, denoted by m+cr(G), is defined as the maximum cardinality of a minimal connected restrained monophonic set of G. We determine bounds for it and certain general properties satisfied by this parameter are studied. It is shown that, for positive integers a, b such that 4≤ a ≤ b , there exists a connected graph G such that  mcr(G) = a and m+cr(G) = b. 

• Referencias bibliográficas
  • F. Buckley and F. Harary, Distance in Graphs. Redwood City, CA: Addison-Wesley, 1990.
  • E. R. Costa, M. C. Dourado, and R. M. Sampaio, “Inapproximability results related to monophonic convexity”, Discrete Applied Mathematics,...
  • M. C. Dourado, F. Protti, and J. L. Szwarcfiter, “Algorithmic aspects of monophonic convexity”, Electronic Notes in Discrete Mathematics,...
  • M. C. Dourado, F. Protti, and J. L. Szwarcfiter, “Complexity results related to monophonic convexity”, Discrete Applied Mathematics, vol....
  • K. Ganesamoorthy and S. Lakshmi Priya, “The Outer Connected Monophonic Number of a Graph”, Ars Combinatoria, vol. 153, pp. 149-160, 2020.
  • K. Ganesamoorthy and S. Lakshmi Priya, “Extreme Outer Connected Monophonic Graphs”, Communications in Combinatorics and Optimization, 2021,...
  • K. Ganesamoorthy and S. Lakshmi Priya, “Further results on the outer connected monophonic number of a graph”, Transactions of National Academy...
  • K. Ganesamoorthy, M. Murugan, and A. P. N. Santhakumaran, “Extreme-support total monophonic graphs”, Bulletin of the Iranian Mathematical...
  • F. Harary, Graph Theory. Addison-Wesley, 1969.
  • E. M. Paluga and S. R. Canoy, Jr, “Monophonic numbers of the join and composition of connected graphs”, Discrete Mathematics, vol. 307, no....
  • A. P. Santhakumaran and P. Titus, “Monophonic Distance in Graphs”, Discrete Mathematics, Algorithms and Applications, vol. 3, no. 2, pp. 159-169,...
  • A. P. Santhakumaran and P. Titus, A Note on “Monophonic Distance in Graphs”, Discrete Mathematics, Algorithms and Applications, vol. 4, no....
  • A. P. Santhakumaran, P. Titus and K. Ganesamoorthy, “On the Monophonic Number of a Graph”, Journal of applied mathematics & informatics,...
  • A. P. Santhakumaran, P. Titus and K. Ganesamoorthy, “The Restrained Monophonic Number of a Graph”, TWMS journal of pure and applied mathematics...
  • A. P. Santhakumaran, P. Titus and K. Ganesamoorthy, “The Connected and Forcing Connected Restrained Monophonic Numbers of a Graph”, Communicated.
  • A. P. Santhakumaran, P. Titus, K. Ganesamoorthy, and M. Murugan, “The forcing total monophonic number of a graph”, Proyecciones (Antofagasta),...
  • A. P. Santhakumaran, T. Venkata Raghu and K. Ganesamoorthy, “Minimal Restrained Monophonic Sets in Graphs”, TWMS journal of pure and applied...