Honeycomb rectangular disks

In this paper, we propose a variation of honeycomb meshes. A honeycomb rectangular disk HReD(m, n) is obtained from the honeycomb rectangular mesh HReM(m, n) by adding a boundary cycle. A honeycomb rectangular disk HReD(m, n) is a 3-regular planar graph. It is obvious that the honeycomb rectangular mesh HReM(m, n) is a subgraph of HReD(m, n). We also prove that HReD(m, n) is hamiltonian. Moreover, HReD(m, n) − f remains hamiltonian for any f ∈ V (HReD(m, n)) ∪ E (HReD(m, n)) if n ⩾ 6.