Ring embedding in faulty honeycomb rectangular torus.
Assume that \(m\) and \(n\) are positive even integers with \(n\geqslant4\). The honeycomb rectangular torus \(HReT(m,n)\) is recognized as another attractive alternative to existing torus interconnection networks in parallel and distributed applications. It is known that any \(HReT(m,n)\) is a 3-regular bipartite graph. We prove that any \(HReT(m,n)-e\) is hamiltonian for any edge \(e\in E(HReT(m,n))\). Moreover, any \(HReT(m,n)-F\) is hamiltonian for any \(F={a,b}\) with \(a\in A\) and \(b\in B\) where \(A\) and \(B\) are the bipartition of \(HReT(m,n),\) if \(n\geqslant6\) or \(m=2.\).
scientific article; zbMATH DE number 1856488