The chromatic polynomial P (G,λ) gives the number of λ-colourings of a graph. If P (G,λ) = P (H1, λ)P (H2, λ)/P (Kr , λ), then the graph G is said to have a chromatic factorisation with chromatic factors H1 and H2. It is known that the chromatic polynomial of any clique-separable graph has a chromatic factorisation. In this paper we construct an infinite family of graphs that have chromatic fac...

the wind as one of the manifestations of renewable energies is very important for tabernacle instead of fossil fuels. the sistan and baluchestan province, according to its topography and position is one of the best places to build wind power plant. in this research, for potential evaluating of the wind power plants construction were considered different criteria and sub-criteria in the province...

We investigate the local chromatic number of shift graphs and prove that it is close to their chromatic number. This implies that the gap between the directed local chromatic number of an oriented graph and the local chromatic number of the underlying undirected graph can be arbitrarily large. We also investigate the minimum possible directed local chromatic number of oriented versions of “topo...

Let P.G; / be the chromatic polynomial of a graph G. A graph G is chromatically unique if for

We present the design of an ultrafast monochromator explicitly designed for extreme-ultraviolet FEL sources, in particular the upcoming FLASH II at DESY. The design originates from the variable-line-spaced (VLS) grating monochromator by adding a second grating to compensate for the pulse-front tilt given by the first grating after the diffraction. The covered spectral range is 6-60 nm, the spec...

Let P (G, λ) be the chromatic polynomial of a graph G. Two graphs G and H are said to be chromatically equivalent, denoted G ∼ H, if P (G, λ) = P (H, λ). We write [G] = {H|H ∼ G}. If [G] = {G}, then G is said to be chromatically unique. In this paper, we first characterize certain complete 6-partite graphs with 6n vertices according to the number of 7-independent partitions of G. Using these re...

Let G be a graph of order n, maximum degree ∆ and minimum degree δ. Let P (G,λ) be the chromatic polynomial of G. It is known that the multiplicity of zero ‘0’ of P (G,λ) is one if G is connected; and the multiplicity of zero ‘1’ of P (G,λ) is one if G is 2-connected. Is the multiplicity of zero ‘2’ of P (G,λ) at most one if G is 3-connected? In this paper, we first construct an infinite family...

1.1 In this note we compute the chromatic polynomial of the Jahangir graph J2p and we prove that it is chromatically unique for p = 3. AMS Subject classification: 05C15

Let P (G, λ) be the chromatic polynomial of a graph G. A graph G is chromatically unique if for any graph H, P (H, λ) = P (G, λ) implies H is isomorphic to G. Liu et al. [Liu, R. Y., Zhao, H. X., Ye, C. F.: A complete solution to a conjecture on chromatic uniqueness of complete tripartite graphs. Discrete Math., 289, 175–179 (2004)], and Lau and Peng [Lau, G. C., Peng, Y. H.: Chromatic uniquene...

It has been suggested that there are two types of chromatic motion mechanisms: signed chromatic motion, in which correspondence across successive frames is based on chromatic content of image regions, and unsigned chromatic motion based on movement of chromatically-defined borders. We investigate whether signed and unsigned red-green chromatic motion are mediated by a genuinely chromatic mechan...