  We show that on cactus graphs the Szeged index is bounded above by twice the
Wiener index. For the revised Szeged index the situation is reversed if the
graph class is further restricted. Namely, if all blocks of a cactus graph are
cycles, then its revised Szeged index is bounded below by twice its Wiener
index. Additionally, we show that these bounds are sharp and examine the cases
of equality. Along the way, we provide a formulation of the revised Szeged
index as a sum over vertices, which proves very helpful, and may be interesting
in other contexts.
