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

In this paper, we investigate a problem on embedding paths into recursive circulant G(2m,4) with faulty elements (vertices and/or edges) and show that each pair of vertices in recursive circulant G(2m,4), m≥3, are joined by a fault-free path of every length from m+1 to |V(G(2m,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(2m,4) has a fault-free cycle of every length from 4 to |V(G(2m,4)∖F)| inclusive excluding 5 passing through an arbitrary fault-free edge for any fault set F with |F|≤m−3.