In this article, we establish the existence of an LHMTS(m v ) for v ≡ 2 (mod 6) and m ≡ 3 (mod 6). Thus there exists an LHMTS(m v ) if and only if v(v − 1)m 2 ≡ 0 (mod 3) except possibly for v = 6, m ≡ 1,5 (mod 6) and m ≠ 1. In the similar way, the existence of LHDTS(m v ) is completely determined, i.e., there exists an LHDTS(m v ) if and only if v(v − 1)m 2 ≡ 0 (mod 3).
Acta Mathematica Sinica, English Series – Springer Journals
Published: May 18, 2018
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