Panconnectivity and Edge-Pancyclicity of Faulty Recursive Circulant G(2 m, 4)

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 cycle of every length from four to |V (G(2 m, 4)\F) | inclusive excluding five passing through an arbitrary fault-free edge for any fault set F with |F | ≤ m − 3