Graphs Chromatic

Fig. 9.—Chromaticity Graph for Various Sugar Liquors, According to the 1931, I. C. I., Standard Observer and Coordinate System.

Each molecule is represented by an ordered -> chromatic graph which describes the topological and chemical nature of each site, i.e. the graph vertices represent nonhydrogen atoms and the edge bonds between these atoms. Vertex chromatism corresponds to the chemical nature of the atoms, edge chromatism to the bond multiplicity. 

Dubois, J.-E. (1976). Ordered Chromatic Graph and Limited Environment Concept. In Chemical Applications of Graph Theory (Balaban, A.T., ed.). Academic Press, New York (NY), pp. 333-370. 

In the DARC/PELCO method (1), the structural variable makes use of graph theory. It is based on simultaneous representation of ail structures (15) whose structural modifications are to be correlated with variations in property and of the population containing these structures. The environment concept is used to describe each structure as an ordered chromatic graph. The principle of syn chronous generation of a structure and of the series which contains it, called hyperstructure is used to describe the population to be studied. This concept and this principle, when applied to an isofocal population, define a multidimensional variable characterizing the chemical structure. 

Figure 5.1. Generation of an ordered chromatic graph G, modelling a structure S...

Dir52] G.A. Dirac, A property of chromatic graphs and some remarks on critical graphs, J. London Math. Soc. 27 (1952), pp. 85-92. 

This method can be used more generally to find what can be called the "unlabelled chromatic polynomial" of a graph — giving the number of ways of coloring in x colors the vertices of a graph when two colorings are equivalent if one is converted to the other by an automorphism of the graph. 

Figure 4.7 Gamut of colors in CIE XYZ space. The chromaticities of light in the visible range from 400 nm to 700 nm form a horseshoe-shaped region. The chromaticities for a black-body radiator at different temperatures is shown in the center. The color of a black-body radiator passes from red at low temperatures through white and on to blue at higher temperatures. The point of equal energy is located at the center of the graph.

Figure 6.20 Results obtained using a two-dimensional gamut-constraint algorithm. The algorithm assumes a single illuminant for the entire image, so we cannot use this algorithm if multiple illuminants are present. The two graphs show the possible illuminants for each image. The Illuminants are displayed as CIE chromaticities.

Figure 6.22 Results obtained using a two-dimensional gamut-constraint algorithm with the assumption that the illuminant can be modeled as a black-body radiator. The two graphs again show the possible illuminants as CIE chromaticities and the illuminant that was selected by the two-dimensional gamut-constraint algorithm.

Figure 6.30 The chromaticity plane is centered on the color of the illuminant. Colors sensed from a surface are located inside a plane spanned by the diffuse color of the object and the color of the illuminant. The graph in (b) shows the projection onto the chromaticity plane.

Figure 7.29 A circle of colors in RGB color space is shown in (a). When we transform data points that are sampled along the circle to log-chromaticity difference space, we obtain the graph in (b).

Figure 7.31 A section from a color Mondrian is shown in (a). The Mondrian contains the colored patches black, white, bright blue, dark blue, yellow, bright green, dank green, and red. Several images of the Mondrian were taken during the course of the day. The graph in (b) shows the x -chromaticities of each patch for all images of the sequence.

Figure 12.17 The images in (a) and (b) show the chromaticities of the actual color of the illuminant. The images in (c) and (d) show the estimated chromaticities. The two graphs in (e) and (f) show the estimated and the actual color of the illuminant for a horizontal line of the image.

Figure 14.1 RGB values and chromaticities computed by the algorithm described in Section 11.2 over all patch reflectances. A red illuminant [1.0, 0.1, 0.1]r is assumed. The graphs (a), (c), and (e) show the RGB results, and the graphs (b), (d), and (f) show the chromaticities. A background reflectance of 0.9 was assumed for the two graphs (a) and (b), a background reflectance of 0.5 was assumed for the two graphs (c) and (d), and a background reflectance of 0.1 was assumed for the two graphs (e) and (f).

A plot of x versus y results in the CIE chromatid ty diagram (Figure 6-6). When the chromaticities of all of the spectral colors are placed in this graph, they form a line called the locus. Within this locus and the line connecting the ends, represented by 400 and 700 nm, every point represents a color that can be made by mixing the three primaries. The point at which exactly equal amounts of each... 

---