2-Exponents of Two-Coloured Lollipops

This paper shows that for an asymmetric primitive two-coloured (n,s)-lollipop on n vertices with s ≤ n; its 2-exponent is at most (s2 -1)/2+(s+1)(n-s). The (n,s)-lollipops whose 2-exponents achieving the bound is characterised and for any asymmetric primitive two-coloured (n,s)-lollipop, a simple algorithm to find its exponent is presented.