  The equator of a graph is the length of a longest isometric cycle. We bound
the order $n$ of a graph from below by its equator $q$, girth $g$ and minimum
degree $\delta$ - and show that this bound is sharp when there exists a Moore
graph with girth $g$ and minimum degree $\delta$. The extremal graphs that
attain our bound give an analogue of Moore graphs. We prove that these extremal
`Moore-like' graphs are regular, and that every one of their vertices is
contained in some maximum length isometric cycle. We show that these extremal
graphs have a highly structured partition that is unique, and easily derived
from any of its maximum length isometric cycles. We characterize the extremal
graphs with girth 3 and 4, and those with girth 5 and minimum degree 3. We also
bound the order of $C_4$-free graphs with given equator and minimum degree, and
show that this bound is nearly sharp. We conclude with some questions and
conjectures further relating our extremal graphs to cages and Moore graphs.
