NAEV图为3—自中心图的充分必要条件及计算机判定

本文证明了一个非邻接离心点(NAEV)图G是3-自中心图,当且仅当G是一个块并且G的每个顶点都有长度为6的最长局部测地圈。本文还给出判定一个图是否为自中心图的算法,以及求出3-NAEV自中心图每个顶点的长度6的局部测地圈算法。

NECESSARY AND SUFFICIENT CONDITIONS FOR A NAEV GRAPH TO BE 3-SELF-CENTERED AND COMPUTER DECISIONS

This paper further shows that an Non-Adjacent Eccentric Vertex graph G is 3-self-centered if and only if G is a block and for each vertex v of G,there is no cycle locally geodesic at v and of length more than 6.Several algorithm? are also given in this paper,whether a graph is self-centered or not which can be decided and the longest locally geodesic cycle of length 6 at each vertex in a 3-NA.EV self-centered graph can be found.