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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  

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  

This study investigates the use of structural similarity index (SSIM) on the minimised side effect to image watermarking. For the fast implementation and more compatibility with the standard discrete cosine transform (DCT)-based codecs, watermark insertion is carried out on the DCT coefficients and hence an SSIM model for DCT-based watermarking is developed. For faster implementation, the SSIM index is maximised over independent 4 × 4 non-overlapped blocks, but the disparity between the adjacent blocks reduces the overall image quality. This problem is resolved through optimisation of overlapped blocks, but, the higher image quality is achieved at a cost of high computational complexity. To... 

Purpose: The purpose of this paper is to describe the use of computational fluid dynamics (CFD) to simulate indoor radon distribution and ventilation effects. This technique was used to predict and visualize radon content and indoor air quality in a one-family detached house in Stockholm. The effects of intake fans, exhaust fans and doors on radon concentration were investigated. Design/methodology/approach: In this study a mechanically balanced ventilation system and a continuous radon monitor (CRM) were used to measure the indoor ventilation rate and radon levels. In a numerical approach, the FLUENT CFD package was used to simulate radon entry into the building and ventilation effects.... 

Radon is released from soil and building materials and can accumulate in residential buildings. Breathing radon and radon progeny for extended periods hazardous to health and can lead to lung cancer. Indoor air conditions and ventilation systems strongly influence indoor radon concentrations. This paper focuses on effects of air change rate, indoor temperature and relative humidity on indoor radon concentrations in a one family detached house in Stockholm, Sweden.In this study a heat recovery ventilation system unit was used to control the ventilation rate and a continuous radon monitor (CRM) was used to measure radon levels. FLUENT, a computational fluid dynamics (CFD) software package was... 

Let $$G$$G be a graph. The core of $$G$$G, denoted by $$G_{Delta }$$GΔ, is the subgraph of $$G$$G induced by the vertices of degree $$Delta (G)$$Δ(G), where $$Delta (G)$$Δ(G) denotes the maximum degree of $$G$$G. A $$k$$k-edge coloring of $$G$$G is a function $$f:E(G)ightarrow L$$f:E(G)→L such that $$|L| = k$$|L|=k and $$f(e_1)e f(e_2)$$f(e1)≠f(e2), for any two adjacent edges $$e_1$$e1 and $$e_2$$e2 of $$G$$G. The chromatic index of $$G$$G, denoted by $$chi '(G)$$χ′(G), is the minimum number $$k$$k for which $$G$$G has a $$k$$k-edge coloring. A graph $$G$$G is said to be Class $$1$$1 if $$chi '(G) = Delta (G)$$χ′(G)=Δ(G) and Class $$2$$2 if $$chi '(G) = Delta (G) + 1$$χ′(G)=Δ(G)+1. Hilton... 

A proper vertex coloring of a graph G is called a dynamic coloring if for every vertex v of degree at least 2, the neighbors of v receive at least two different colors. Assume that ch2 (G) is the minimum number k such that for every list assignment of size k to each vertex of G, there is a dynamic coloring of G such that every vertex is colored with a color from its list. In this paper, it is proved that if G is a graph with no component isomorphic to C5 and Δ (G) ≥ 3, then ch2 (G) ≤ Δ (G) + 1, where Δ (G) is the maximum degree of G. This generalizes a result due to Lai, Montgomery and Poon which says that under the same assumptions χ2 (G) ≤ Δ (G) + 1. Among other results, we determine ch2... 

Long Reed-Solomon codes over the prime field GF(216 + 1) are proposed as a low overhead channel code for reliable transmission of video over noisy and lossy channels. The added redundancy is near optimal from the information theoretic point of view contrary to the conventionally used intra-coding and sync (marker) insertion in video transmission that are not justified theoretically. Compared to known source-channel coding methods, we have achieved the quality of the output of source coder by providing nearly error free transmission. (By nearly error free we mean an arbitrarily small error probability.) The price paid for such remarkable video quality improvement and relatively low complexity... 

A hybrid video codec, where the intraframe pictures are wavelet-based coded and the interframe pictures are coded with a standard H.263 codec is proposed. We show that intraframe-wavelet coded pictures not only improve the quality of I-pictures but also result in lower distorted prediction pictures that outperforms a pure H.263 video codec. © 2005 IEEE  

Packet loss recovery is an important part of P2P video streaming networks due to inevitable packet loss in today's internet and interdependency of data units in compressed video streams. In addition, the architecture of P2P streaming networks, in which the data delivered to the receivers through chain of peers, can intensify the impact of the internet packet loss on the quality of perceived video at the receivers. FEC and ARQ are the two most important techniques that can be used to overcome the side effect of the internet packet loss in P2P video streaming networks. Based on these two techniques, different packet loss recovery strategies can be applied in different overlay hops of a given... 

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  

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... 

Suppose that G is a graph and f: V (G) → ℕ is a labeling of the vertices of G. Let S(v) denote the sum of labels over all neighbors of the vertex v in G. A labeling f of G is called lucky if S(u) ≠ S(v) for every pair of adjacent vertices u and v. Also, for each vertex v ∈ V(G), let L(v) denote a list of natural numbers available at v. A list lucky labeling, is a lucky labeling f such that f(v) ∈ L(v) for each v ∈ V(G). A graph G is said to be lucky k-choosable if every k-list assignment of natural numbers to the vertices of G permits a list lucky labeling of G. The lucky choice number of G, ηl(G), is the minimum natural number k such that G is lucky k-choosable. In this paper, we prove that... 

In this paper, a new method for spatial concealment of missing areas in image and video signals transmitted over error prone infrastructures, is presented. The concealment process is performed in three steps. First, a novel technique is used to estimate the significant edges of missing areas after performing a directional edge analysis on the correctly received neighboring blocks of the missing areas. This technique uses the moments of the neighboring edge magnitudes to obtain an adaptive threshold for rejecting non-significant directions. Second, based on the predicted significant directions, an approximation is obtained for each missing pixel. Finally, for each pixel, we compute a weighted... 

A proper vertex k-coloring of a graph G is called dynamic, if there is no vertex v∈V(G) with d(v)<2 and all of its neighbors have the same color. The smallest integer k such that G has a k-dynamic coloring is called the dynamic chromatic number of G and denoted by χ2(G). We say that v∈V(G) in a proper vertex coloring of G is a bad vertex if d(v)<2 and only one color appears in the neighbors of v. In this paper, we show that if G is a graph with the chromatic number at least 6, then there exists a proper vertex χ(G)-coloring of G such that the set of bad vertices of G is an independent set. Also, we provide some upper bounds for χ2(G)- χ(G) in terms of some parameters of the graph G  

In this study, a method for enhancing low-contrast images is proposed. This method, called Gaussian mixture model-based contrast enhancement (GMMCE), brings into play the Gaussian mixture modelling of histograms to model the content of the images. On the basis of the fact that each homogeneous area in natural images has a Gaussian-shaped histogram, it decomposes the narrow histogram of low-contrast images into a set of scaled and shifted Gaussians. The individual histograms are then stretched by increasing their variance parameters, and are diffused on the entire histogram by scattering their mean parameters, to build a broad version of the histogram. The number of Gaussians as well as their... 

In this paper joint optimization of layers in the layered video coding is investigated. Through theoretical analysis and simulations, it is shown that, due to higher interactions between the layers in a SNR scalable codec, this type of layering technique benefits most from joint optimization of the layers. A method for joint optimization is then proposed, and its compression efficiency is contrasted against the separate optimization and an optimized single layer coder. It is shown that, in joint optimization of SNR scalable coders when the quantization step size of the enhancement layer is larger than half the step size of the base layer, an additional improvement is gained by not sending... 

Let G be a graph and χl (G) denote the list chromatic number of G. In this paper we prove that for every graph G for which the length of each cycle is divisible by l (l ≥ 3), χl (G) ≤ 3. © 2008 Elsevier B.V. All rights reserved  

Let G be a graph and f: V (G) → ℕ be a function. An f-coloring of a graph G is an edge coloring such that each color appears at each vertex v ∈ 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 χʹf(G). It was shown that for every graph G, Δf(G) ≤ χʹf(G) ≤ Δf(G) + 1, where Δf(G) = maxv ∈V (G)(formula presented). A graph G is said to be f-Class 1 if χʹf(G) = Δf(G), and f-Class 2, otherwise. Also, GΔfis the induced subgraph of G on (formula presented). In this paper, we show that if G is a connected graph with Δ(GΔf) ≤ 2 and G has an edge cut of size at most Δf(G) − 2 which is a star, then G is f-Class 1. Also, we... 

One of the most important challenges in target parameters estimation via model-free methods is selection of the most effective input parameters namely features selection (FS). Indeed, irrelevant features can degrade the estimation performance. In the current study, the challenge of choosing among the several plant parameters is tackled by means of the innovative FS algorithm named ranking of features with minimum deviation from the target parameter (RFMD). The selected features accompanied with the stable and the fast learning algorithm of multilayer perceptron (MLP) neural network (i.e. Levenberg-Marquardt algorithm) which is a combination of gradient descent and Gauss-newton learning...