4.6 Article

Hypercube embeddings and Cayley graphs generated by transpositions

期刊

MATHEMATICAL METHODS IN THE APPLIED SCIENCES
卷 45, 期 11, 页码 7227-7237

出版社

WILEY
DOI: 10.1002/mma.8233

关键词

bubble sort graph; graph; isometric embedding; partial cube

资金

  1. National Natural Science Foundation of China [11571155, 11961067, 12071194]

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This paper studies a class of Cayley graphs generated by transpositions and proves that this class of graphs is a partial cube if and only if it is a bubble sort graph. Furthermore, analytical expressions for the Wiener indices of bubble sort graphs are provided.
A graph is called a partial cube if it can be embedded into a hypercube isometrically. In this paper, we study a class of Cayley graphs-Cayley graphs generated by transpositions-and show that a Cayley graph Gamma generated by transpositions is a partial cube if and only if Gamma is a bubble sort graph. This result enhances a result of Alahmadi et al. in 2016: BSn is a partial cube. As a corollary, we give the analytical expressions of the Wiener indices of bubble sort graphs.

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