▁no ▁ 8 - g ons ▁of ▁the ▁generalized ▁quad rangle ▁G Q ( 2 , 2 ). ▁It ▁is ▁named ▁after ▁R . ▁M . ▁F oster , ▁whose ▁F oster ▁census ▁of ▁cub ic ▁symmetric ▁graphs ▁included ▁this ▁graph . ▁ ▁The ▁b ipart ite ▁half ▁of ▁the ▁F oster ▁graph ▁is ▁a ▁distance - regular ▁graph ▁and ▁a ▁locally ▁linear ▁graph . ▁It ▁is ▁one ▁of ▁a ▁finite ▁number ▁of ▁such ▁graphs ▁with ▁degree ▁six . ▁ ▁Al gebra ic ▁properties ▁The ▁autom orphism ▁group ▁of ▁the ▁F oster ▁graph ▁is ▁a ▁group ▁of ▁order ▁ 4 3 2 0 . ▁It ▁acts ▁trans it ively ▁on ▁the ▁vertices , ▁on ▁the ▁edges ▁and ▁on ▁the ▁ar cs ▁of ▁the ▁graph . ▁Therefore , ▁the ▁F oster ▁graph ▁is ▁a ▁symmetric ▁graph . ▁It ▁has ▁autom orph isms ▁that ▁take ▁any ▁vertex ▁to ▁any ▁other ▁vertex ▁and ▁any ▁edge ▁to ▁any ▁other ▁edge . ▁According ▁to ▁the ▁F oster ▁census , ▁the ▁F oster ▁graph , ▁referenced ▁as ▁F 9 0 A , ▁is ▁the ▁only ▁cub ic ▁symmetric ▁graph ▁on ▁ 9 0 ▁vertices . ▁ ▁The ▁characteristic ▁polynomial ▁of ▁the ▁F oster ▁graph ▁is ▁equal ▁to ▁. ▁ ▁Gallery ▁ ▁References ▁ ▁. ▁ ▁. ▁ ▁. ▁ ▁Category : Ind ividual ▁graphs ▁Category : Reg ular ▁graphs <0x0A> </s> ▁The ▁P inn ar oo ▁C emetery ▁and ▁C rem ator ium ▁is ▁a ▁c emetery ▁and ▁cre m ator ium ▁located ▁at ▁Graham ▁Road , ▁Br id