▁graphs ▁have ▁the ▁same ▁T ut te ▁polynomial , ▁but ▁the ▁con verse ▁is ▁not ▁true . ▁For ▁example , ▁the ▁T ut te ▁polynomial ▁of ▁every ▁tree ▁on ▁ ▁edges ▁is ▁. ▁ ▁T ut te ▁polynomials ▁are ▁often ▁given ▁in ▁tab ular ▁form ▁by ▁listing ▁the ▁coefficients ▁ ▁of ▁ ▁in ▁row ▁ ▁and ▁column ▁. ▁For ▁example , ▁the ▁T ut te ▁polynomial ▁of ▁the ▁Peters en ▁graph , ▁ ▁is ▁given ▁by ▁the ▁following ▁table . ▁ ▁Other ▁example , ▁the ▁T ut te ▁polynomial ▁of ▁the ▁oct ah ed ron ▁graph ▁is ▁given ▁by ▁ ▁History ▁W . ▁T . ▁T ut te ’ s ▁interest ▁in ▁the ▁delet ion – cont raction ▁formula ▁started ▁in ▁his ▁under grad uate ▁days ▁at ▁Tr inity ▁College , ▁Cambridge , ▁originally ▁motiv ated ▁by ▁perfect ▁rect angles ▁and ▁sp anning ▁trees . ▁He ▁often ▁applied ▁the ▁formula ▁in ▁his ▁research ▁and ▁“ w onder ed ▁if ▁there ▁were ▁other ▁interesting ▁functions ▁of ▁graphs , ▁invariant ▁under ▁isomorphism , ▁with ▁similar ▁recursion ▁formula e .” ▁R . ▁M . ▁F oster ▁had ▁already ▁observed ▁that ▁the ▁chrom atic ▁polynomial ▁is ▁one ▁such ▁function , ▁and ▁T ut te ▁began ▁to ▁discover ▁more . ▁His ▁original ▁termin ology ▁for ▁graph ▁invari ants ▁that ▁satisfy ▁the ▁delet ion – cont raction ▁recursion ▁was ▁W - function , ▁and ▁V - function ▁if ▁multip lic ative ▁over ▁components . ▁T ut te ▁writes , ▁“ Play ing ▁with ▁my ▁W - functions ▁I ▁obtained