%0 Journal Article
%T 直径为3且有割边的已约简图<br>Reduced Graphs of Diameter Three and Having Cut Edges
%A 冶福龙
%A 秦晓晓
%J Pure Mathematics
%P 3193-3197
%@ 2160-7605
%D 2023
%I Hans Publishing
%R 10.12677/PM.2023.1311331
%X 若图H = (V(H)，E(H)) 的任意一个偶子集 R？V(H)，H 有一个生成连通子图H<sub>R</sub>，使得O(H<sub>R</sub>) = S,则H 是可折叠的，Catlin 证明任意图 G 都有唯一的两两点不交的极大可折叠子图的集合。G 的约简记为 G\"，是将 G 中的每一个极大可折叠子图收缩成一个点后得到的图，若G = G\"，则 G 是已约简的。在本文中主要刻画直径为3 且有割边的已约简图。若割边是非平凡的，则 G？S\"<sub>n,m</sub>; 否则,除 1 度点外其余点都在一个导出i-圈,i ∈{4,5}。<br />
A graph H = (V(H)，E(H)) is collapsible if for every subset R？V(H) with |R| even, H has a spanning connected sungraph H<sub>R</sub> such that O(H<sub>R</sub>) = R. Catlin showed that every graph G has unique collection of pairwise vertex-disjoint maximal collapsible subgraphs. The reduction of G, denoted by G\", is the graph obtained from G by contracting each maximal collapsible subgraphs into a single vertex. A graph G is
reduced if G = G\". In this article, we characterize the reduced graphs of diameter three and having cut edges. If the cute edge is nontrival, then G？S\"<sub>n,m</sub>, otherwise, all vertices in an induced i-cycle, except 1 degree vertices, i ∈{4,5}.
%K 直径，可折叠图，已约简图<br>Diameter
%K Collapsible Graph
%K Reduced Graph
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=75627