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On minimum vertex covers of generalized petersen graphs

Behsaz, B ; Sharif University of Technology | 2008

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  1. Type of Document: Article
  2. Publisher: 2008
  3. Abstract:
  4. For natural numbers n and k (n > 2k), a generalized Petersen graph P(n, k), is defined by vertex set {ui ui] and edge set {ui ui+1, ui ui, ui ui+k}; where i = 1, 2,..., n and subscripts are reduced modulo n. Here first, we characterize minimum vertex covers in generalized Petersen graphs. Second, we present a lower bound and some upper bounds for β(P(n, k)), the size of minimum vertex cover of P(n,k). Third, in some cases, we determine the exact values of β(P(n,k)). Our conjecture is that β(P(n, k)) < n+ [n/5], for all n and k
  5. Keywords:
  6. Domination number ; Paired-domination ; Critical graph
  7. Source: Australasian Journal of Combinatorics ; Volume 40 , 2008 , Pages 253-264 ; 10344942 (ISSN)
  8. URL: https://ajc.maths.uq.edu.au/pdf/40/ajc_v40_p253.pdf