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On the size of graphs whose cycles have length divisible by a fixed integer

Akbari, S ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. Publisher: 2009
  3. Abstract:
  4. Let G be a simple graph of order n and size m which is not a tree. If ℓ; ≤ 3 is a natural number and the length of every cycle of G is divisible by ℓ, then m ≤l/l-2 (n -2), and the equality holds if and only if the following hold: (i) ℓ is odd and G is a cycle of order ℓ or (ii) ℓ is even and G is a generalized 6>-graph with paths of length |l/2 It is shown that for a (0 mod ℓ)-cycle graph, m/n < l/l-1 if ℓ is odd, and for a given e > 0, there exists a (0 mod ℓ)-cycle graph G with m/n > l/l-2 - e. Also m/n > l/l-2 if ℓ is even, and for a given e > 0, there exists a (0 mod ℓ)-cycle graph G with m/n l/l-2-e
  5. Keywords:
  7. Source: Australasian Journal of Combinatorics ; Volume 45 , 2009 , Pages 67-72 ; 10344942 (ISSN)
  8. URL: https://ajc.maths.uq.edu.au/pdf/45/ajc_v45_p067.pdf