A family of tetravalent half-arc-transitive graphs

Alspach et al. (J. Austral. Math. Soc. 56(3) (1994) 391-402) constructed an infinite family of tetravalent graphs M(a; m, n) and proved that if n >= 9 be odd and a(3) equivalent to 1(mod n), then M(a; 3, n) is half-arc-transitive. In this paper, we show that if a(3) equivalent to 1(mod n), then M(a; 3, n) is an infinite family of tetravalent half-arc-transitive Cayley graphs for all integers n except 7 and 14.