GraphPeriphery
GraphPeriphery[g] gives vertices that are maximally distant to at least one vertex in the graph g.
GraphPeriphery[{v -> w, ...}] uses rules to specify the graph g.
Examples
Find the periphery of a graph:
GraphPeriphery[CycleGraph[6]]
(* {1, 2, 3, 4, 5, 6} *)Periphery of a path graph:
GraphPeriphery[PathGraph[{a, b, c, d, e}]]
(* {a, e} *)Please visit the official Wolfram Language Reference for more details.