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The adjacent vertex distinguishing total chromatic number

Authors: Coker, Tom; Johannson, Karen R;

The adjacent vertex distinguishing total chromatic number

Abstract

A well-studied concept is that of the total chromatic number. A proper total colouring of a graph is a colouring of both vertices and edges so that every pair of adjacent vertices receive different colours, every pair of adjacent edges receive different colours and every vertex and incident edge receive different colours. This paper considers a strengthening of this condition and examines the minimum number of colours required for a total colouring with the additional property that for any adjacent vertices $u$ and $v$, the sets of colours incident to $u$ is different from the set of colours incident to $v$. It is shown that there is a constant $C$ so that for any graph $G$, there exists such a colouring using at most $Δ(G) + C$ colours.

Country
United Kingdom
Keywords

proper total colouring, Coloring of graphs and hypergraphs, chromatic number, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), adjacent vertex distinguishing, Proper total colouring, 510, Theoretical Computer Science

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    influence
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
23
Top 10%
Top 10%
Average
Green
hybrid