Maximum induced subgraph of a recursive circulant

  • Authors:
  • Xiaofan Yang;David J. Evans;Graham M. Megson

  • Affiliations:
  • Department of Computer Science and Technology, Chongqing University, Chongqing, P.R. China;Parallelism, Algorithms and Architectures Research Centre, Department of Computer Science, Loughborough University, Loughborough, Leicestershire, UK;Department of Computer Science, School of Systems Engineering, University of Reading, Whiteknights, Reading, Berkshire, UK

  • Venue:
  • Information Processing Letters
  • Year:
  • 2005

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Abstract

The recursive circulant RC(2n, 4) enjoys several attractive topological properties. Let max_εG(m) denote the maximum number of edges in a subgraph of graph G induced by m nodes. In this paper, we show that max_εRC(2n, 4)(m) = Σi=0r(Pi/2 + i)2pi. where p0 p1 ... pr are nonnegative integers defined by m = Σi=0r 2Pi . We then apply this formula to find the bisection width of RC(2n,4). The conclusion shows that, as n-dimensional cube. RC(2n, 4) enjoys a linear bisection width.