A graph H is said to be a double star(simply DS)if H consists of two disjoint stars K 1,m 1 ,K 1,m 2 together with an edge between a vertex in K 1,m 1 anda vertex in K 1,m 2 which have the maximum degrees in K 1,m 1 and K 1,m 2 respectively.

• 一个图H称为一个双星 (DoubleStar) ；当H由 2个不交的星K1；m1 、K1；m2 加上连接它们最大度点的一条边所构成 .