Circular coloring of signed graphs
نویسندگان
چکیده
منابع مشابه
Coloring Signed Graphs
This survey paper provides an introduction to signed graphs, focusing on coloring. We shall introduce the concept of signed graphs, a proper coloring, and basic properties, such as a balanced graph and switchings. We will examine the chromatic number for six special signed graphs, upper bound the chromatic number, and discuss practical applications of signed graphs.
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Given a graph G with nonnegative node labels w, a multiset of stable sets S1, . . . , Sk ⊆ V (G) such that each vertex v ∈ V (G) is contained in w(v) many of these stable sets is called a weighted coloring. The weighted coloring number χw(G) is the smallest k such that there exist stable sets as above. We provide a polynomial time combinatorial algorithm that computes the weighted coloring numb...
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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 ...
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A signed graph is a graph where the edges are assigned either positive ornegative signs. Net degree of a signed graph is the dierence between the number ofpositive and negative edges incident with a vertex. It is said to be net-regular if all itsvertices have the same net-degree. Laplacian energy of a signed graph is defined asε(L(Σ)) =|γ_1-(2m)/n|+...+|γ_n-(2m)/n| where γ_1,...,γ_n are the ei...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2017
ISSN: 0364-9024
DOI: 10.1002/jgt.22147