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On the defining sets of some special graphs

Mahmoodian, E. S ; Sharif University of Technology | 2006

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  1. Type of Document: Article
  2. Publisher: 2006
  3. Abstract:
  4. In a given graph G, a set S of vertices with an assignment of colors to them is a defining set of vertex coloring for G, if there exists a unique extension of the colors of 5 to a X(G)-coloring of the vertices of G. A defining set with minimum cardinality is called a smallest defining set (of vertex coloring) and its cardinality, the defining number, is denoted by d(G,X)- Mahmoodian et al. (1999) determined the defining number of graph C3 × Cn. In this paper, we study the defining number of graph Cm × Cn, and show that Also, we prove a similar result for the defining number of graph Cn × Pn
  5. Keywords:
  7. Source: Australasian Journal of Combinatorics ; Volume 35 , 2006 , Pages 69-81 ; 10344942 (ISSN)
  8. URL: https://ajc.maths.uq.edu.au/pdf/35/ajc_v35_p069.pdf