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Silver Block Intersection Graphs of Steiner 2-Designs

Ahadi, A ; Sharif University of Technology | 2013

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  1. Type of Document: Article
  2. DOI: 10.1007/s00373-012-1174-y
  3. Publisher: 2013
  4. Abstract:
  5. For a block design D, a series of block intersection graphs G i, or i-BIG(D), i = 0,..., k is defined in which the vertices are the blocks of D, with two vertices adjacent if and only if the corresponding blocks intersect in exactly i elements. A silver graph G is defined with respect to a maximum independent set of G, called an α-set. Let G be an r-regular graph and c be a proper (r + 1)-coloring of G. A vertex x in G is said to be rainbow with respect to c if every color appears in the closed neighborhood N[x] = N(x) ∪ {x}. Given an α-set I of G, a coloring c is said to be silver with respect to I if every x ∈ I is rainbow with respect to c. We say G is silver if it admits a silver coloring with respect to some I. Finding silver graphs is of interest, for a motivation and progress in silver graphs see Ghebleh et al. (Graphs Combin 24(5):429-442, 2008) and Mahdian and Mahmoodian (Bull Inst Combin Appl 28:48-54, 2000). We investigate conditions for 0-BIG(D) and 1-BIG(D) of Steiner 2-designs D=S(2,k,v) to be silver
  6. Keywords:
  7. Block intersection graph ; Silver coloring ; Steiner 2-design ; Steiner triple system
  8. Source: Graphs and Combinatorics ; Volume 29, Issue 4 , 2013 , Pages 735-746 ; 09110119 (ISSN)
  9. URL: http://link.springer.com/article/10.1007%2Fs00373-012-1174-y