证明了a=4时,Gvozdjak猜想成立.即路Pn存在一个(a,b;n)-优美标号,当且仅当整数a,b,n满足:(1)b-a与n(n+1)/2有相同的奇偶性;(2)0〈|b-a|≤(n+1)/2;(3)n/2≤a+b≤3n/2.在a=4时,成立.
The following conjecture is posed by Gvozdjak:An(a,b;n)-graceful labeling of Pn exists if and only if the integers a,b,n satisfy:(1)b-a has the same parity as n(n+1)/2;(2)0|b-a|≤(n+1)/2;(3)n/2≤a+b≤3n/2.The conjecture is true when a=4.