一些图的下完美邻域数上界

Upper Bound of Lower Perfect Neighborhood Number of Some Graphs

研究了图G的一类特殊控制数:下完美邻域数G.证明了在n阶连通图G中,若G不含圈或仅含点不交的圈,则Gn3.同时对n阶t叉树T分层,证明了其下完美邻域数上界Tt2+nt+1.

Mainly studies a kind of special dominating parameter： the lower perfect neighborhood number θ（G）. Proved that ifa connected graph G with n order is cycle-free or contains vertexthen θ（G）≤[n/3] and gvies the upper bound θ（T） ≤n/t^2＋t＋1 by using the method disjoined cycles, of dividing the vertexes of tree into levels.