ArticleOriginal scientific text
Title
Vertex-distinguishing edge-colorings of linear forests
Authors 1, 1
Affiliations
- AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland
Abstract
In the PhD thesis by Burris (Memphis (1993)), a conjecture was made concerning the number of colors c(G) required to edge-color a simple graph G so that no two distinct vertices are incident to the same multiset of colors. We find the exact value of c(G) - the irregular coloring number, and hence verify the conjecture when G is a vertex-disjoint union of paths. We also investigate the point-distinguishing chromatic index, χ₀(G), where sets, instead of multisets, are required to be distinct, and determine its value for the same family of graphs.
Keywords
irregular edge-coloring, vertex-distinguishing edge-coloring, point-distinguishing chromatic index
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Pages:
95-103
Main language of publication
English
Received
2008-05-12
Accepted
2009-04-03
Published
2010
DOI: 10.7151/dmgt.1479
Exact and natural sciences