منابع مشابه
Coloring of integer distance graphs
An integer distance graph is a graph G(D) with the set of integers as vertex set and with an edge joining two vertices u and v if and only if ju ? vj 2 D where D is a subset of the positive integers. We determine the chromatic number (D) of G(D) for some nite distance sets D such as sets of consecutive integers and special sets of cardinality 4.
متن کاملDistance Graphs and T-Coloring
We discuss relationships among T-colorings of graphs and chromatic numbers, fractional chromatic numbers, and circular chromatic numbers of distance graphs. We first prove that for any finite integral set T that contains 0, the asymptotic T-coloring ratio R(T ) is equal to the fractional chromatic number of the distance graph G(Z, D), where D=T&[0]. This fact is then used to study the distance ...
متن کامل2-distance Coloring of Sparse Graphs
A 2-distance coloring of a graph is a coloring of the vertices such that two vertices at distance at most 2 receive distinct colors. We prove that every graph with maximum degree Δ at least 4 and maximum average degree less that 73 admits a 2-distance (Δ + 1)-coloring. This result is tight. This improves previous known results of Dolama and Sopena.
متن کاملCircular Coloring for Graphs with Distance Constraints
Let G = (V,E) be a simple un-weighted graph, and let → d= (d1, d2, · · ·, dm) be a sequence of positive reals. For a positive real r, let Sr denote the circle on R 2 centered at the origin with circumference r. A circular r−coloring for G with distance constraint → d is a mapping f : V (G) → Sr such that |f(u) − f(v)|r ≥ di, whenever the distance between u and v in G is i (where |x− y|r is the ...
متن کاملOn the distance eigenvalues of Cayley graphs
In this paper, we determine the distance matrix and its characteristic polynomial of a Cayley graph over a group G in terms of irreducible representations of G. We give exact formulas for n-prisms, hexagonal torus network and cubic Cayley graphs over abelian groups. We construct an innite family of distance integral Cayley graphs. Also we prove that a nite abelian group G admits a connected...
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ژورنال
عنوان ژورنال: Acta Mathematica Sinica, English Series
سال: 2014
ISSN: 1439-8516,1439-7617
DOI: 10.1007/s10114-014-3238-9