# Special Kinds of Colorable Complements in Graphs

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In this paper we investigate the minimum number of colors required for a proper edge coloring of a finite, undirected, regular graph G in which no two adjacent vertices are incident to edges colored with the same set of colors. In particular, we study this parameter in relation to the direct...

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coloring of vertices of a graph G is called r-perfect, if the color structure of each ball of radius r in G depends only on the color of the center of the ball. The parameters of a perfect coloring are given by the matrix A = ( a), where n is the number of colors and a is the number of vertices...

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Considering the partitions of a set into nonempty subsets, we obtain an expression for the number of all partitions of a given type. The chromatic polynomial of a graph subdivision is generalized, considering two sets of colors, and a general explicit expression is obtained for this...

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In this paper we determine the equitable total chromatic number Î§et for the double star graph K1,n,n and the fan graph Fm,n.

- CHARACTERIZATION OF SIMPLE ORBIT GRAPHS. // Acta Mathematica Universitatis Comenianae;2010, Vol. 79 Issue 2, p175
No abstract available.

- On dominator colorings in graphs. ARUMUGAM, S; BAGGA, JAY; CHANDRASEKAR, K // Proceedings of the Indian Academy of Sciences: Mathematical Scie;Nov2012, Vol. 122 Issue 4, p561
A dominator coloring of a graph G is a proper coloring of G in which every vertex dominates every vertex of at least one color class. The minimum number of colors required for a dominator coloring of G is called the dominator chromatic number of G and is denoted by Ï‡( G). In this paper we...

- Algebraic Integers as Chromatic and Domination Roots. Alikhani, Saeid; Hasni, Roslan // International Journal of Combinatorics;2012, p1
Let G be a simple graph of order n and Î» âˆˆ N. A mapping f : V (G) â†’ {1, 2, . . . , Î»} is called a Î»-colouring of G if f(u) # f(v) whenever the vertices u and v are adjacent in G. The number of distinct Î»-colourings of G, denoted by P(GÎ»), is called the chromatic...

- Monochromatic and Heterochromatic Subgraphs in Edge-Colored Graphs - A Survey. Kano, Mikio; Xueliang Li // Graphs & Combinatorics;Nov2008, Vol. 24 Issue 4, p237
Nowadays the term monochromatic and heterochromatic (or rainbow, multicolored) subgraphs of an edge-colored graph appeared frequently in literature, and many results on this topic have been obtained. In this paper, we survey results on this subject. We classify the results into the following...

- THE b-DOMATIC NUMBER OF A GRAPH. FAVARON, ODILE // Discussiones Mathematicae: Graph Theory;2013, Vol. 33 Issue 4, p747
Besides the classical chromatic and achromatic numbers of a graph related to minimum or minimal vertex partitions into independent sets, the b-chromatic number was introduced in 1998 thanks to an alternative definition of the minimality of such partitions. When independent sets are replaced by...