Vertex-distinguishing edge-colorings of linear forests | Zendy

Sylwia Cichacz | Zendy; Jakub Przybyło | Zendy

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Vertex-distinguishing edge-colorings of linear forests

Author(s) -

Sylwia Cichacz,

Jakub Przybyło

Publication year - 2010

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.1479

Subject(s) - mathematics , combinatorics , edge coloring , multiset , conjecture , vertex (graph theory) , simple graph , discrete mathematics , graph , graph power , line graph

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 nd the exact value of c(G) | the irregular coloring number, and hence verify the conjecture when G is a vertexdisjoint union of paths. We also investigate the point-distinguishing chromatic index, 0(G), where sets, instead of multisets, are required to be distinct, and determine its value for the same family of graphs.

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