On strongly Z(2s+1)-connected graphs
On strongly Z(2s+1)-connected graphs
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在强 Z(2s 1) 连接图上
DOI：
10.1016/j.dam.2014.03.017
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发表时间：
2014
影响因子：
1.1
通讯作者：
Zhang Zhao
中科院分区：
文献类型：
--
作者：
Lai Hong-Jian;Liang Yanting;Liu Juan;Meng Jixiang;Miao Zhengke;Shao Yehong;Zhang Zhao
图G的一个定向是mod（2s + 1）-定向，如果在这个定向下，每个顶点的净出度全等于零mod（2s + 1）.如果对于任何函数B：V（G）→ Z2 s+ 1满足∑ v∈ V（G）B（v）<$0（mod 2s + 1），G总有一个定向D使得每个顶点v的网出度与B（v）mod（2s + 1）全等，则G是强Z2 s+ 1-连通的.本文证明了连通图有mod（2s + 1）-定向当且仅当它是（2s + 1）-正则二部图的收缩图。我们还证明了每个（4 s− 1）-边连通串并联图是强Z2 s+ 1-连通的，每个简单4 p-连通弦图是强Z2 s+ 1-连通的.
An orientation of a graph G is a mod (2 s+ 1)-orientation if under this orientation, the net out-degree at every vertex is congruent to zero mod (2 s+ 1). If for any function b: V (G)→ Z 2 s+ 1 satisfying∑ v∈ V (G) b (v)≡ 0 (mod 2 s+ 1), G always has an orientation D such that the net out-degree at every vertex v is congruent to b (v) mod (2 s+ 1), then G is strongly Z 2 s+ 1-connected. In this paper, we prove that a connected graph has a mod (2 s+ 1)-orientation if and only if it is a contraction of a (2 s+ 1)-regular bipartite graph. We also proved that every (4 s− 1)-edge-connected series–parallel graph is strongly Z 2 s+ 1-connected, and every simple 4 p-connected chordal graph is strongly Z 2 s+ 1-connected.