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Let G be a simple undirected uniquely vertex k-colorable graph, or a k-UCG for short. M. Truszczyński [Some results on uniquely colorable graphs, in Finite and Infinite Sets, North-Holland, Amsterdam, 1984, pp. 733--748] introduced $e^{^{*}}(G)=|V(G)|(k-1)-{k \choose 2}$ as the minimum number of edges for a k-UCG and S. J. Xu [J. Combin. Theory Ser. B, 50 (1990), pp. 319--320] conjectured that any minimal k-UCG contains a Kk as a subgraph. In this paper, first we introduce a technique called forcing. Then by applying this technique in conjunction with a feedback structure we construct a k-UCG with clique number k-t, for each $t \geq 1$ and each k, when k is large enough. This also... 

Scheduling sports leagues has drawn significant attention to itself in recent years, as it involves considerable revenue as well as challenging combinatorial optimization problems. A particular class of these problems is the Traveling Tournament Problem (TTP) which focuses on minimizing the total traveling distance for teams. In this paper, an efficient simulated annealing approach is presented for TTP which applies two simultaneous and disparate models for the problem in order to search the solutions space more effectively. Also, a computationally efficient modified greedy scheme is proposed for constructing a favorable initial solution for the simulated annealing algorithm. Our... 

Absorption and fluorescence spectra of three Sudan dyes (Sudan III, SudanIV and Sudan black B) were recorded in various solvents with different polarity in the range of 300-800 nm, at room temperature. The solvatochromic method was used to investigate dipole moments of these dyes in ground and excited states, in different media. The solvatochromic behavior of these substances and their solvent-solute interactions were analyzed via solvent polarity parameters. Obtained results express the effects of solvation on tautomerism and molecular configuration (geometry) of Sudan dyes in solvent media with different polarity. Furthermore, analyze of solvent-solute interactions and value of ground and... 

Let (Formula presented.) be a graph of order (Formula presented.) and size (Formula presented.). Suppose that (Formula presented.) is a function such that (Formula presented.). In this paper we provide a criterion for (Formula presented.)-choosability of (Formula presented.). Using this criterion, it is shown that the choice number of the complete (Formula presented.)-partite graph (Formula presented.) is (Formula presented.), which is a well-known result due to Erdös, Rubin and Taylor. Among other results we study the (Formula presented.)-choosability of the complete (Formula presented.)-partite graphs with part sizes at most (Formula presented.), when (Formula presented.), for every vertex... 

The kinetics of coalescence is studied experimentally using a new technique for tracking the process in the bulk phase. For this aim, aqueous solutions of KSCN (colorless) and FeCl3 (light yellow) are used to make individual W/O emulsions. Any coalescence occurred between drops containing KSCN solution and those containing FeCl3 solution would combine these solutions. This leads to a reddish brown solution due to the formation of iron(III)thiocyanate. The intensity change of this red color with time represents the dynamics of coalescence occurring between drops of different emulsified aqueous droplets. The detector response to any changes in the system is recorded as a function of time. In... 

Let G be a graph. It is well-known that G contains a proper vertex-coloring with χ(G) colors with the property that at least one color class of the coloring is a dominating set in G. Among all such proper vertex-coloring of the vertices of G, a coloring with the maximum number of color classes that are dominating sets in G is called a dominating-χ-coloring of G. The number of color classes that are dominating sets in a dominating-χ-coloring of G is defined to be the dominating-χ-color number of G and is denoted by dχ(G). In this paper, we prove that if G is a claw-free graph with minimum degree at least two, then dχ(G)≥2  

Let G and H be two graphs. A proper vertex coloring of G is called a dynamic coloring, if for every vertex v with degree at least 2, the neighbors of v receive at least two different colors. The smallest integer k such that G has a dynamic coloring with k colors denoted by χ2(G). We denote the cartesian product of G and H by G□H. In this paper, we prove that if G and H are two graphs and δ(G) ≥ 2, then χ2(G□H) ≤ max(χ2(G),x(H)). We show that for every two natural numbers m and n, m,n ≥ 2, χ2(Pm□Pn) = 4. Also, among other results it is shown that if 3|mn, then χ2(C m□Cn) = 3 and otherwise χ2(C m□Cn) = 4  

The magnetic adsorbent nanoparticle was modified using cationic surface active agent. Zinc ferrite nanoparticle and cetyl trimethylammonium bromide were used as an adsorbent and a surface active agent, respectively. Dye removal ability of the surface modified nanoparticle as an adsorbent was investigated. Direct Green 6(DG6), Direct Red 31 (DR31) and Direct Red 23 (DR23) were used. The characteristics of the adsorbent were studied using Fourier transform infrared (FTIR), scanning electron microscopy (SEM) and X-ray diffraction (XRD). The effect of adsorbent dosage, initial dye concentration and salt was evaluated. In ternary system, dye removal of the adsorbent at 90, 120, 150 and 200 mg/L... 

A proper vertex coloring of a graph G is called a dynamic coloring if for every vertex ν with degree at least 2, the neighbors of ν receive at least two different colors. It was conjectured that if G is a regular graph, then χ2(G) - χ (G) ≤ 2. In this paper we prove that, apart from the cycles C4 and C5 and the complete bipartite graphs Kn,n, every strongly regular graph G, satisfies χ2(G) - χ (G) ≤ 1  

Let G be a graph. The core of G, denoted by GΔ, is the subgraph of G induced by the vertices of degree Δ(G), where Δ(G) denotes the maximum degree of G. A k -edge coloring of G is a function f: E(G) → L such that {pipe}L{pipe} = k and f(e1) ≠ f(e2) for all two adjacent edges e1 and e2 of G. The chromatic index of G, denoted by χ′(G), is the minimum number k for which G has a k-edge coloring. A graph G is said to be Class 1 if χ′(G) = Δ(G) and Class 2 if χ′(G) = Δ(G) + 1. In this paper it is shown that every connected graph G of even order whose core is a cycle of order at most 13 is Class 1  

In this paper, we study the problem of online conflict-free coloring of intervals on a line, where each newly inserted interval must be assigned a color upon insertion such that the coloring remains conflict-free, i.e. for each point p in the union of the current intervals, there must be an interval I with a unique color among all intervals covering p. We first present a simple algorithm which uses O(√n) colors where n is the number of current intervals. Next, we propose an CF-coloring of intervals which uses O(log3 n) colors  

Segmentation of aerial images has been a challenging task in recent years. This paper introduces a simple and efficient method for segmentation and classification of aerial images based on a pixel-level classification. To this end, we use the Gabor texture features in HSV color space as our best experienced features for aerial images segmentation and classification. We test different classifiers including KNN, SVM and a classifier based on sparse representation. Comparison of our proposed method with a sample of segmentation pre-process based classification methods shows that our pixel-wise approach results in higher accuracy results with lower computation time  

For a given set of n colored points with k colors in the plane, we study the problem of computing the smallest color-spanning axis-parallel square. First, for a dynamic set of colored points on the real line, we propose a dynamic structure with O(log2 n) update time per insertion and deletion for maintaining the smallest color-spanning interval. Next, we use this result to compute the smallest color-spanning square. Although we show there could be Ω(kn) minimal color-spanning squares, our algorithm runs in O(nlog2 n) time and O(n) space  

Routers and routing protocols are critical parts of a network infrastructure. OSPF is one of the most important routing protocols, and therefore its vulnerabilities can be very destructive. This makes its security analysis critical. There are many reported and potential vulnerabilities in OSPF protocol. Considering the complexity and the ambiguity of its description in RFC 2328, it is very valuable to design a formal model of the protocol and analyze the vulnerabilities of its critical parts. In this paper, some challenging parts of OSPF protocol along with attack scenarios are modeled by means of Colored Petri Net in CPN Tools environment. Then, the reported vulnerabilities are analyzed by... 

We propose a new system which can generate digital holograms using natural color information. The proposed system can generate about 10 digital holographic video frames per a second using about 6K light sources  

Existing algorithms based on scale invariant feature transform (SIFT) and Harris corners such as edge-driven dual-bootstrap iterative closest point and Harris-partial intensity invariant feature descriptor (PIIFD) respectivley have been shown to be robust in registering multimodal retinal images. However, they fail to register color retinal images with other modalities in the presence of large content or scale changes. Moreover, the approaches need preprocessing operations such as image resizing to do well. This restricts the application of image registration for further analysis such as change detection and image fusion. Motivated by the need for efficient registration of multimodal retinal... 

Let G be a graph. The minimum number of colors needed to color the edges of G is called the chromatic index of G and is denoted by x0(G). It is well known that δ(G) ≤ x0(G) ≤ δ(G) + 1, for any graph G, whereδ(G) denotes the maximum degree of G. A graph G is said to be class 1 if x0(G) = δ(G) and class 2 if x0(G) = δ(G)+1. Also, Gδ is the induced subgraph on all vertices of degreeδ(G). Let f : V(G) ! N be a function. An f -coloring of a graph G is a coloring of the edges of E(G) such that each color appears at each vertex v 2 V(G) at most f (v) times. The minimum number of colors needed to f -color G is called the f -chromatic index of G and is denoted by x0f (G). It was shown that for every... 

A proper orientation of a graph G=(V,E) is an orientation D of E(G) such that for every two adjacent vertices v and u, dD -(v) ≠ dD -(u) where dD -(v) is the number of edges with head v in D. The proper orientation number of G is defined as χ→(G)=minD∈Γmaxv∈V(G)d D -(v) where Γ is the set of proper orientations of G. We have χ(G)-1≤χ→(G)≤Δ(G), where χ(G) and Δ(G) denote the chromatic number and the maximum degree of G, respectively. We show that, it is NP-complete to decide whether χ→(G)=2, for a given planar graph G. Also, we prove that there is a polynomial time algorithm for determining the proper orientation number of 3-regular graphs. In sharp contrast, we will prove that this problem... 

A proper labeling of a graph is an assignment of integers to some elements of a graph, which may be the vertices, the edges, or both of them, such that we obtain a proper vertex coloring via the labeling subject to some conditions. The problem of proper labeling offers many variants and received a great interest during recent years. We consider the algorithmic complexity of some variants of the proper labeling problems, we present some polynomial time algorithms and NP-completeness results for them  

The fish freshness was evaluated using machine vision technique through color changes of eyes and gills of farmed and wild gilthead sea bream (Sparus aurata), being employed lightness (L*), redness (a *), yellowness (b*), chroma (c *), and total color difference (ΔE) parameters during fish ice storage. A digital color imaging system, calibrated to provide accurate CIELAB color measurements, was employed to record the visual characteristics of eyes and gills. The region of interest was automatically selected using a computer program developed in MATLAB software. L*, b *, and ΔE of eyes increased with storage time, while c* decreased. The a* parameter of fish eyes did not show clear a trend...