一类图族的匹配唯一性

The matching uniqueness of a classes of graphs

证明了图族m2P2∪m3P3∪[∪i≥2m2iP2i]∪dD4∪[∪j≥3njCj]∪tT1,2,3∪sT1,2,4匹配唯一。当且仅当dm2=dm3=n3t=n3n5s=n15t=n5n9s=mknk+1=0(k≥2),其中m2,m3,m2i(i≥2),d,nj(j≥3),t,s都是非负整数。

At present paper,the matching uniqueness of a classes of graphs,that is m_2P_2∪m_3P_3∪[∪(i≥2)m_(2i)P_(2i)]∪dD_4∪[∪(j≥3)n_jC_j]∪tT_(1,2,3)∪sT_(1,2,4)was proved only if dm_2=dm_3=n_3t=n_3n_5s=n_(15)t=n_5n_9s=m_kn_(k+1)=0(k≥2)where m_2,m_3,m_(2i)(i≥2),d,n_j(j≥3),t,s are nonnegative integers.