摘要
Let q be a positive integer.The graphs,called the q-trees are defined by recursion:the smallest q-tree is the complete graph K_q with q vertices,and a q-tree with n+1 vertices where n≥q is obtained by adding a new vertex adjacent to each of q arbitrarily selected but mutually adjacent vertices of q-tree with n vertices.Obviously,1-trees are the graphs which are generally called trees.In this paper,it is proved that for any positive integer q,q-tree is reconstructible.
q 是一个正整数,所谓 q-树的图是递归定义的:最小的 q-树是完全图 K_q,一个 n+1阶的 q-树是通过在 n 阶 q-树上加上一个新点并连接这点与 n 阶 q-树中任意 q 个互相邻接的点而获得,其中 n≥q.1-树我们通常称为树.在本文中,证明了对任意正整数 q,q-树是可重构的.
