Hamiltonian Properties of Hybrid-Faulty Burnt Pancake Graphs

We investigate the combined occurrence of edge faults and vertex faults in the burnt pancake graph ($B{P}_n$). In this paper, we prove that $B{P}_n-F$, where $F$ includes pairs of end-vertices of matching edges and fault-tolerant edges, contains a Hamiltonian cycle when $\mathrm{\mid }F\mathrm{\mid }\le n-2$ and a Hamiltonian path when $\mathrm{\mid }F\mathrm{\mid }\le n-3$. This establishes that $B{P}_n$ is $(n-2)$-hybrid fault Hamiltonian and $(n-3)$-hybrid fault Hamiltonian connected for $n\ge 3$. These results are demonstrated to be optimal under the given conditions, with all bounds shown to be tight.