Abstract
Let T1, T2 be spanning trees in a graph G. If for any two vertices u, v of G, the paths from u to v in T1, T2 are vertex-disjoint except end vertices u and v, then T1, T2 are called two completely independent spanning trees (CISTs for short) in Pai and Chang [12] proposed an approach to recursively construct two CISTs in several hypercube-variant networks, including crossed cubes. For every kind of n-dimensional variant cube, the diameters of two CISTs for their construction are 2n − 1. In this paper, we give a new algorithm to construct two CISTs T1 and T2 in n-dimensional crossed cubes, and show that diam(T1) = diam(T2) = 2n − 2 if n ∈ {4,5}; and diam(T1) = diam(T2) = 2n − 3 if n ≥ 6 where diam(G) is the diameter of graph G.
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Acknowledgments
This research was partially supported by MOST grants 107-2221-E-131-011 from the Ministry of Science and Technology, Taiwan.
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Pai, KJ. (2019). Designing an Algorithm to Improve the Diameters of Completely Independent Spanning Trees in Crossed Cubes. In: Chang, CY., Lin, CC., Lin, HH. (eds) New Trends in Computer Technologies and Applications. ICS 2018. Communications in Computer and Information Science, vol 1013. Springer, Singapore. https://doi.org/10.1007/978-981-13-9190-3_46
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DOI: https://doi.org/10.1007/978-981-13-9190-3_46
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