In the Fouth International Graph Conference

G.S.Bloom et.al.proposed thefollowing problem:How many Euler trails there are in a complete graph K2n+1. Uptonow we know that there are one Euler chain in a complete graph K3 and 22Euler trails in a complete graph K5.It is still an open problem that how manyEulerian trails are there n a complete graph K_(2(?)+1)(n≥3).This paper used aavailable method to thow that there are 541568 Eulerian trails in a complete graphK7.Based on this computing

we show that there are 180 544 Eulerian Cycles in acomplele graph K7

and give an upper bound of the number of Eulerian Chains'in complete graphs K2n+1 (n≥4).