Paper Info
Title
The Distinguishing Index of Infinite Graphs.
Abstract
The distinguishing index D '(G) of a graph G is the least cardinal d such that G has an edge colouring with d colours that is only preserved by the trivial automorphism. This is similar to the notion of the distinguishing number D(G) of a graph G, which is defined with respect to vertex colourings. We derive several bounds for infinite graphs, in particular, we prove the general bound D '(G) <= Delta(G) for an arbitrary infinite graph. Nonetheless, the distinguishing index is at most two for many countable graphs, also for the infinite random graph and for uncountable tree-like graphs. We also investigate the concept of the motion of edges and its relationship with the Infinite Motion Lemma.
Year
Venue
Keywords
2015
ELECTRONIC JOURNAL OF COMBINATORICS
distinguishing index,automorphism,infinite graph,countable graph,edge colouring,Infinite Motion Lemma
Field
DocType
Volume
Graph automorphism,Random regular graph,Discrete mathematics,Combinatorics,Vertex-transitive graph,Line graph,Forbidden graph characterization,Symmetric graph,Universal graph,1-planar graph,Mathematics
Journal
22.0
Issue
ISSN
Citations 
1.0
1077-8926
2
PageRank 
References 
Authors
0.44
4
2
Name
Order
Citations
PageRank
Izak Broere114331.30
Monika Pilsniak220.44