On the local distinguishing chromatic number
نویسندگان
چکیده
منابع مشابه
The Distinguishing Chromatic Number
In this paper we define and study the distinguishing chromatic number, χD(G), of a graph G, building on the work of Albertson and Collins who studied the distinguishing number. We find χD(G) for various families of graphs and characterize those graphs with χD(G) = |V (G)|, and those trees with the maximum chromatic distingushing number for trees. We prove analogs of Brooks’ Theorem for both the...
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Collins and Trenk define the distinguishing chromatic number χD(G) of a graph G to be the minimum number of colors needed to properly color the vertices of G so that the only automorphism of G that preserves colors is the identity. They prove results about χD(G) based on the underlying graphG. In this paper we prove results that relate χD(G) to the automorphism group of G. We prove two upper bo...
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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
متن کاملLocal Chromatic Number and Distinguishing the Strength of Topological Obstructions
The local chromatic number of a graph G is the number of colors appearing in the most colorful closed neighborhood of a vertex minimized over all proper colorings of G. We show that two specific topological obstructions that have the same implications for the chromatic number have different implications for the local chromatic number. These two obstructions can be formulated in terms of the hom...
متن کاملThe distinguishing chromatic number of bipartite graphs of girth at least six
The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has a vertex labeling with $d$ labels that is preserved only by a trivial automorphism. The distinguishing chromatic number $chi_{D}(G)$ of $G$ is defined similarly, where, in addition, $f$ is assumed to be a proper labeling. We prove that if $G$ is a bipartite graph of girth at least six with the maximum ...
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ژورنال
عنوان ژورنال: AKCE International Journal of Graphs and Combinatorics
سال: 2019
ISSN: 0972-8600,2543-3474
DOI: 10.1016/j.akcej.2018.01.007