Are Arthropodium and Peraphyllum in the same family?
no
Title: Dichopogon
Passage: Dichopogon is a genus of perennial herbs, native to Australia and New Guinea.  It is included in the genus "Arthropodium" by some authorities, although recognized as a distinct genus by others.  In the APG III classification system, it is placed in the family Asparagaceae, subfamily Lomandroideae (formerly the family Laxmanniaceae).
Title: Peraphyllum
Passage: Peraphyllum is a monotypic genus of flowering plants in the rose family, containing the single species Peraphyllum ramosissimum, commonly known as the squaw apple or wild crab apple.
Title: Arthropodium
Passage: Arthropodium is a genus of herbaceous perennial plants in the subfamily Lomandroideae of the family Asparagaceae.  It is native to Australia, New Zealand, New Caledonia and Madagascar.
Peraphyllum Arthropodium