Panconnectivity of locally twisted cubes. (English) Zbl 1118.05050
Summary: The locally twisted cube \(LTQ_{n}\) which is a newly introduced interconnection network for parallel computing is a variant of the hypercube \(Q_{n}\). X. Yang et al. [Appl. Math. Lett. 17, 919–925 (2004; Zbl 1056.05074)] proved that \(LTQ_{n}\) is Hamiltonian connected and contains a cycle of length from 4 to \(2^{n}\) for \(n \geq 3\). In this work, we improve this result by showing that for any two different vertices \(u\) and \(v\) in \(LTQ_{n}\) \((n \geq 3)\), there exists a \(uv\)-path of length \(l\) with \(d(u,v)+2 \leq l \leq 2^{n} - 1\) except for a shortest \(uv\)-path.
Citations:
Zbl 1056.05074References:
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