Graphs with Large Distinguishing Chromatic Number
نویسندگان
چکیده
منابع مشابه
Graphs with Large Distinguishing Chromatic Number
The distinguishing chromatic number χD(G) of a graph G is the minimum number of colours required to properly colour the vertices of G so that the only automorphism of G that preserves colours is the identity. For a graph G of order n, it is clear that 1 6 χD(G) 6 n, and it has been shown that χD(G) = n if and only if G is a complete multipartite graph. This paper characterizes the graphs G of o...
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A labeling f : V (G) → {1, 2, . . . , d} of the vertex set of a graph G is said to be proper d-distinguishing if it is a proper coloring of G and any nontrivial automorphism of G maps at least one vertex to a vertex with a different label. The distinguishing chromatic number of G, denoted by χD(G), is the minimum d such that G has a proper d-distinguishing labeling. Let χ(G) be the chromatic nu...
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An adjacent vertex distinguishing edge-coloring or an avd-coloring of a simple graph G is a proper edge-coloring of G such that no pair of adjacent vertices meets the same set of colors. We prove that every graph with maximum degree ∆ and with no isolated edges has an avd-coloring with at most ∆ + 300 colors, provided that ∆ > 1020. AMS Subject Classification: 05C15
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2013
ISSN: 1077-8926
DOI: 10.37236/2407