Independent Spanning Trees on Special BC Networks

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There is a well-known conjecture on independent spanning trees (ISTs) on graphs: For any n-connected graph G with n≥1, there are n ISTs rooted at an arbitrary node on G. It still remains open for n≥5. We propose an integrated algorithm to construct n ISTs rooted at any node similar to 0 or 10n-1 on n-dimensional HCH cube for n≥1 and give the simulations of ISTs on several special BC networks, such as HCH cubes, crossed cubes, Möbius cubes, twisted cubes, etc.