Before revision:  In this paper, we investigate the extent to which FP and ES can differ, characterise tree shapes on which the indices are identical, and provide a new, shorter proof that FP and SV are identical on rooted trees .
After revision:  In this paper, we investigate the extent to which FP and ES can differ, characterise tree shapes on which the indices are identical, and study the equivalence of FP and SV are identical on rooted trees .