Some characterization theorems on dominating chromatic partition-covering number of graphs

• Michael Raj, L. Benedict ^[1] ; Ayyaswamy, S. K. ^[2]
  1. [1] St. Joseph's College New York

     St. Joseph's College New York

     Estados Unidos

     
  2. [2] SASTRA University

     SASTRA University

     India

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 33, Nº. 1, 2014, págs. 13-23
• Idioma: inglés
• DOI: 10.4067/S0716-09172014000100002
• Enlaces
  • Texto completo
• Resumen

  • Let G = (V, E) be a graph of order n = |V| and chromatic number (G) A dominating set D of G is called a dominating chromatic partition-cover or dcc-set, if it intersects every color class of every X-coloring of G. The minimum cardinality of a dcc-set is called the dominating chromatic partition-covering number, denoted dcc(G). The dcc-saturation number equals the minimum integer i such that every vertex ν ∈ V is contained in a dcc-set of cardinality k.This number is denoted by dccs(G) In this paper we study a few properties ofthese two invariants dcc(G) and dccs(G)

• Referencias bibliográficas
  • Citas [1] B. D. Acharya, The Strong Domination Number of a Graph and Related Concepts, Jour. Math. Phy. Sci. 14, no. 5, pp. 471—475, (1980).
  • [2] S. Arumugam and R. Kala, Domsaturation Number of a Graph, Indian J. Pure. Appl. Math. 33, no. 11, pp. 1671—1676, (2002).
  • [3] L. Benedict Michael Raj, S. K. Ayyaswamy, and S. Arumugam, Chromatic Transversal Domination in Graphs, J. Comb. Math. Comb. Computing,...
  • [4] G. Chartrand and P. Zang, Chromatic Graph Theory, CRC Press, Boca Raton, FL, (2009).
  • [5] F. Harary, Graph Theory, Addison-Wesley, Reading, Mass, (1969).
  • [6] F. Harary, S. Hedetneimi and R. Robinson, Uniquely Colorable Graphs, J. Combin. Theory 6, pp. 264-270, (1969).
  • [7] T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Domination in Graphs: Advanced Topics, Marcel Dekker Inc., (1998).
  • [8] , Fundamentals of Domination in Graphs, Marcel Dekker Inc., (1998).
  • [9] O. Ore, Theory of Graphs, Amer. Math. Soc. Colloq. Publ. 38, (Amer. Math Soc., Providence, RI), (1962).