Panconnectivity and edge-pancyclicity of faulty recursive circulant G(2m,4)

Jung-Heum Park
2008 Theoretical Computer Science  
In this paper, we investigate a problem on embedding paths into recursive circulant G(2 m , 4) with faulty elements (vertices and/or edges) and show that each pair of vertices in recursive circulant G(2 m , 4), m ≥ 3, are joined by a fault-free path of every length from m + 1 to |V (G(2 m , 4) \ F)| − 1 inclusive for any fault set F with |F| ≤ m − 3. The bound m − 3 on the number of acceptable faulty elements is the maximum possible. Moreover, recursive circulant G(2 m , 4) has a fault-free
more » ... e of every length from 4 to |V (G(2 m , 4)\ F)| inclusive excluding 5 passing through an arbitrary fault-free edge for any fault set F with |F| ≤ m −3.
doi:10.1016/j.tcs.2007.10.016 fatcat:5myzwl36urffjiqpxtv3imsaea