Paper Info
Title
Group connectivity in line graphs
Abstract
Tutte introduced the theory of nowhere zero flows and showed that a plane graph G has a face k-coloring if and only if G has a nowhere zero A-flow, for any Abelian group A with |A|=k. In 1992, Jaeger et al. [9] extended nowhere zero flows to group connectivity of graphs: given an orientation D of a graph G, if for any b:V(G)@?A with @?\"v\"@?\"V\"(\"G\")b(v)=0, there always exists a map f:E(G)@?A-{0}, such that at each v@?V(G), @?e=vw is directed from v to wf(e)-@?e=uv is directed from u to vf(e)=b(v) in A, then G is A-connected. Let Z\"3 denote the cyclic group of order 3. In [9], Jaeger et al. (1992) conjectured that every 5-edge-connected graph is Z\"3-connected. In this paper, we proved the following. (i)Every 5-edge-connected graph is Z\"3-connected if and only if every 5-edge-connected line graph is Z\"3-connected. (ii)Every 6-edge-connected triangular line graph is Z\"3-connected. (iii)Every 7-edge-connected triangular claw-free graph is Z\"3-connected. In particular, every 6-edge-connected triangular line graph and every 7-edge-connected triangular claw-free graph have a nowhere zero 3-flow.
Year
DOI
Venue
2011
10.1016/j.disc.2011.07.017
Discrete Mathematics
Keywords
Field
DocType
line graphs,nowhere zero flows,triangular graphs,claw-free graphs,group connectivity,line graph,connected graph,cyclic group,abelian group,plane graph,claw free graph
Discrete mathematics,Combinatorics,Edge-transitive graph,Vertex-transitive graph,Graph power,Bound graph,Cubic graph,Regular graph,Distance-regular graph,Mathematics,Voltage graph
Journal
Volume
Issue
ISSN
311
20
0012-365X
Citations 
PageRank 
References 
0
0.34
14
Authors
5
Name
Order
Citations
PageRank
Hong-Jian Lai163197.39
Hao Li252.52
Ping Li3217.14
Yanting Liang4225.81
Senmei Yao562.35