▁p ter yg op al at ine ▁gang l ion . ▁ ▁Add itional ▁Im ages ▁ ▁See ▁also ▁▁ ▁Tr ig em inal ▁n erve ▁ ▁C ran ial ▁n erves ▁ ▁References ▁ ▁Books ▁ ▁External ▁links ▁▁▁▁ ▁() ▁ ▁* ▁Category : Tr ig em inal ▁n erve <0x0A> </s> ▁In ▁the ▁mathematical ▁field ▁of ▁graph ▁theory , ▁the ▁F oster ▁graph ▁is ▁a ▁b ipart ite ▁ 3 - regular ▁graph ▁with ▁ 9 0 ▁vertices ▁and ▁ 1 3 5 ▁edges . ▁ ▁The ▁F oster ▁graph ▁is ▁Hamiltonian ▁and ▁has ▁chrom atic ▁number ▁ 2 , ▁chrom atic ▁index ▁ 3 , ▁radius ▁ 8 , ▁diameter ▁ 8 ▁and ▁g irth ▁ 1 0 . ▁It ▁is ▁also ▁a ▁ 3 - ver tex - connected ▁and ▁ 3 - edge - connected ▁graph . ▁It ▁has ▁queue ▁number ▁ 2 ▁and ▁the ▁upper ▁bound ▁on ▁the ▁book ▁thick ness ▁is ▁ 4 . ▁ ▁All ▁the ▁cub ic ▁distance - regular ▁graphs ▁are ▁known . ▁The ▁F oster ▁graph ▁is ▁one ▁of ▁the ▁ 1 3 ▁such ▁graphs . ▁It ▁is ▁the ▁unique ▁distance - trans itive ▁graph ▁with ▁intersection ▁array ▁{ 3 , 2 , 2 , 2 , 2 , 1 , 1 , 1 ; 1 , 1 , 1 , 1 , 2 , 2 , 2 , 3 }. ▁It ▁can ▁be ▁constructed ▁as ▁the ▁inc idence ▁graph ▁of ▁the ▁partial ▁linear ▁space ▁which ▁is ▁the ▁unique ▁triple ▁cover ▁with