On r-Hued Coloring of Hypercubes

For positive integers k and r,a(k,r)-coloring of graph G is a proper vertex k-coloring of G such that the neighbors of any vertex v∈V(G)receive at least min{d_(G)(v),r}different colors.The r-hued chromatic number of G,denoted χ_(r)(G),is the smallest integer k such that G admits a(k,r)-coloring.Let Q_(n) be the n-dimensional hypercube.For any integers n and r with n≥2 and 2≤r≤5,we investigated the behavior of χ_(r)(Q_(n)),and determined the exact value of χ_(2)(Q_(n))and χ_(3)(Q_(n))for all positive integers n.

A Cognitive Psychological Study on the Acquisition of Chinese Word’s Coloring Meaning--Chinese as a Second Language

Lexical meaning mainly includes rational meaning,grammatical meaning,and coloring meaning.Mastering the coloring meaning of vocabulary is of great significance for foreign students to use Chinese vocabulary correctly.This study mainly examines the psychological mechanism of Chinese second language learners mastering the coloring meaning of words,examines the psychological characteristics of students mastering the color meaning of words from the perspectives of second language learning theory and cognitive theory,establishes a cognitive schema for coloring meaning learning,and proposes corresponding learning models and teaching strategies.

High corrosion resistance of electroless Ni-P with chromium-free conversion pre-treatments on AZ91D magnesium alloy

Phosphate-manganese, tannic acid and vanadium conversion coatings were proposed as an effective pre-treatment layer between electroless Ni-P coating and AZ91D magnesium alloy substrate to replace the traditional chromate plus HF pre-treatment. The electrochemical results show that the chrome-free coatings plus electroless Ni-P coating on the magnesium alloy has the lowest corrosion current density and most positive corrosion potential compared with chromate plus electroless Ni-P coating on the magnesium alloy. These proposed pre-treatment layers on the substrate reduce the corrosion of magnesium during plating process, and reduce the potential difference between the matrix and the second phase. Thus, an electroless Ni-P coating with fine crystalline and dense structure was obtained, with preferential phosphorus content, low porosity, good corrosion-resistance and strengthened adhesion than the chromate plus electroless Ni-P.

Vertex-distinguishing E-total Coloring of Complete Bipartite Graph K 7,n when7≤n≤95

Let G be a simple graph. A total coloring f of G is called an E-total coloring if no two adjacent vertices of G receive the same color, and no edge of G receives the same color as one of its endpoints. For an E-total coloring f of a graph G and any vertex x of G, let C（x） denote the set of colors of vertex x and of the edges incident with x, we call C（x） the color set of x. If C（u） ≠ C（v） for any two different vertices u and v of V （G）, then we say that f is a vertex-distinguishing E-total coloring of G or a VDET coloring of G for short. The minimum number of colors required for a VDET coloring of G is denoted by Хvt^e（G） and is called the VDE T chromatic number of G. The VDET coloring of complete bipartite graph K7,n （7 ≤ n ≤ 95） is discussed in this paper and the VDET chromatic number of K7,n （7 ≤ n ≤ 95） has been obtained.

Vertex-distinguishing VE-total Colorings of Cycles and Complete Graphs

Let G be a simple graph of order at least 2.A VE-total-coloring using k colors of a graph G is a mapping f from V (G) E(G) into {1,2,···,k} such that no edge receives the same color as one of its endpoints.Let C(u)={f(u)} {f(uv) | uv ∈ E(G)} be the color-set of u.If C(u)=C(v) for any two vertices u and v of V (G),then f is called a k-vertex-distinguishing VE-total coloring of G or a k-VDVET coloring of G for short.The minimum number of colors required for a VDVET coloring of G is denoted by χ ve vt (G) and it is called the VDVET chromatic number of G.In this paper we get cycle C n,path P n and complete graph K n of their VDVET chromatic numbers and propose a related conjecture.

A Method for Trust Management in Cloud Computing: Data Coloring by Cloud Watermarking

With the development of Internet technology and human computing, the computing environment has changed dramatically over the last three decades. Cloud computing emerges as a paradigm of Internet computing in which dynamical, scalable and often virtuMized resources are provided as services. With virtualization technology, cloud computing offers diverse services （such as virtual computing, virtual storage, virtual bandwidth, etc.） for the public by means of multi-tenancy mode. Although users are enjoying the capabilities of super-computing and mass storage supplied by cloud computing, cloud security still remains as a hot spot problem, which is in essence the trust management between data owners and storage service providers. In this paper, we propose a data coloring method based on cloud watermarking to recognize and ensure mutual reputations. The experimental results show that the robustness of reverse cloud generator can guarantee users＇ embedded social reputation identifications. Hence, our work provides a reference solution to the critical problem of cloud security.

Vertex-distinguishing IE-total Colorings of Cycles and Wheels

Let G be a simple graph. An IE-total coloring f of G refers to a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color. Let C（u） be the set of colors of vertex u and edges incident to u under f. For an IE-total coloring f of G using k colors, if C（u）=C（v） for any two different vertices u and v of V （G）, then f is called a k-vertex-distinguishing IE-total-coloring of G, or a k-VDIET coloring of G for short. The minimum number of colors required for a VDIET coloring of G is denoted by χievt（G）, and is called the VDIET chromatic number of G. We get the VDIET chromatic numbers of cycles and wheels, and propose related conjectures in this paper.

On the adjacent vertex-distinguishing acyclic edge coloring of some graphs

A proper edge coloring of a graph G is called adjacent vertex-distinguishing acyclic edge coloring if there is no 2-colored cycle in G and the coloring set of edges incident with u is not equal to the coloring set of edges incident with v, where uv∈ E（G）. The adjacent vertex distinguishing acyclic edge chromatic number of G, denoted by X＇Aa（G）, is the minimal number of colors in an adjacent vertex distinguishing acyclic edge coloring of G. If a graph G has an adjacent vertex distinguishing acyclic edge coloring, then G is called adjacent vertex distinguishing acyclic. In this paper, we obtain adjacent vertex-distinguishing acyclic edge coloring of some graphs and put forward some conjectures.

New mixed broadcast scheduling approach using neural networks and graph coloring in wireless sensor network

Due to the mutual interference and sharing of wireless links in TDMA wireless sensor networks, conflicts will occur when data messages are transmitting between nodes. The broadcast scheduling problem （BSP） is aimed to schedule each node in different slot of fixed length frame at least once, and the objective of BSP is to seek for the optimal feasible solution, which has the shortest length of frame slots, as well as the maximum node transmission. A two-stage mixed algorithm based on a fuzzy Hopfield neural network is proposed to solve this BSP in wireless sensor network. In the first stage, a modified sequential vertex coloring algorithm is adopted to obtain a minimal TDMA frame length. In the second stage, the fuzzy Hopfleld network is utilized to maximize the channel utilization ratio. Experimental results, obtained from the running on three benchmark graphs, show that the algorithm can achieve better performance with shorter frame length and higher channel utilizing ratio than other exiting BSP solutions.

Vertex-distinguishing Total Colorings of 2Cn

Let f be a proper total k-coloring of a simple graph G. For any vertex x ∈ V（G）, let Cf（x） denote the set of colors assigned to vertex x and the edges incident with x. If Cf（u） ≠ Cf（v） for all distinct vertices u and v of V（G）, then f is called a vertex- distinguishing total k-coloring of G. The minimum number k for which there exists a vertex- distinguishing total k-coloring of G is called the vertex-distinguishing total chromatic number of G and denoted by Xvt（G）. The vertex-disjoint union of two cycles of length n is denoted by 2Cn. We will obtain Xvt（2Cn） in this paper.

THE INFLUENCE OF COMPOSITION AND TEMPERATURE OF BATH ANDAFTER-TREATMENT 0N COLORATION IN COLORING HOT DIPGALVANIZATION

The 08 Al steel sheets were hot dip ped into Zn - Mn bath with 0 1 % Mn and 0 2 % Mn at600 ～420 ℃ bath tem perature , and then w ere treated in different w ays . The after - treat ments include cooling in the air at room tem perature directly , holding at the upper part of thehot dip galvanizing furnace for 60 s an d then holding at 510 ±10 ℃for 90 s . The results in dicated that blue , yellow , and purple , w hose coloration varied with the co m position an d thetem perature of bath and the w ays of after - treat ment . Finally , the mechanism of coloredzinc coating w as discussed .

Vertex-distinguishing IE-total Colorings of Complete Bipartite Graphs K8,n

Let G be a simple graph. An IE-total coloring f of G is a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color. For each vertex x of G, let C(x) be the set of colors of vertex x and edges incident to x under f. For an IE-total coloring f of G using k colors, if C(u) ≠ C(v) for any two different vertices u and v of G, then f is called a k-vertex-distinguishing IE-total-coloring of G or a k-VDIET coloring of G for short. The minimum number of colors required for a VDIET coloring of G is denoted by χ_(vt)^(ie) (G) and is called vertex-distinguishing IE-total chromatic number or the VDIET chromatic number of G for short. The VDIET colorings of complete bipartite graphs K_(8,n)are discussed in this paper. Particularly, the VDIET chromatic number of K_(8,n) are obtained.

A SEVEN-COLOR THEOREM ON EDGE-FACE COLORING OF PLANE GRAPHS

Melnikov(1975) conjectured that the edges and faces of a plane graph G can be colored with △(G) + 3 colors so that any two adjacent or incident elements receive distinct colors, where △(G) denotes the maximum degree of G. This paper proves the conjecture for the case △(G) ≤4.

Adjacent Vertex-distinguishing E-total Coloring on Some Join Graphs Cm V Gn

Let G(V, E) be a simple connected graph and k be positive integers. A mapping f from V∪E to {1, 2, ··· , k} is called an adjacent vertex-distinguishing E-total coloring of G(abbreviated to k-AVDETC), if for uv ∈ E(G), we have f(u) ≠ f(v), f(u) ≠ f(uv), f(v) ≠ f(uv), C(u) ≠C(v), where C(u) = {f(u)}∪{f(uv)|uv ∈ E(G)}. The least number of k colors required for which G admits a k-coloring is called the adjacent vertex-distinguishing E-total chromatic number of G is denoted by x^e_(at) (G). In this paper, the adjacent vertexdistinguishing E-total colorings of some join graphs C_m∨G_n are obtained, where G_n is one of a star S_n , a fan F_n , a wheel W_n and a complete graph K_n . As a consequence, the adjacent vertex-distinguishing E-total chromatic numbers of C_m∨G_n are confirmed.

Cyclically Interval Total Coloring of the One Point Union of Cycles

A total coloring of a graph G with colors 1, 2, ..., t is called a cyclically interval total t-coloring if all colors are used, and the edges incident to each vertex v∈V(G) together with v are colored by (dG(v)+1) consecutive colors modulo t, where dG(v) is the degree of the vertex v in G. The one point union ?of k-copies of cycle Cn is the graph obtained by taking v as a common vertex such that any two distinct cycles? and? are edge disjoint and do not have any vertex in common except v. In this paper, we study the cyclically interval total colorings of , where n≥3 and k≥2.

Cyclically Interval Total Colorings of Cycles and Middle Graphs of Cycles

A total coloring of a graph G is a functionsuch that no adjacent vertices, edges, and no incident vertices and edges obtain the same color. A k-interval is a set of k consecutive integers. A cyclically interval total t-coloring of a graph G is a total coloring a of G with colors 1,2,...,t, such that at least one vertex or edge of G is colored by i,i=1,2,...,t, and for any, the set is a -interval, or is a -interval, where dG(x) is the degree of the vertex x in G. In this paper, we study the cyclically interval total colorings of cycles and middle graphs of cycles.

Research of Privacy Preservation Method Based on Data Coloring

In the cloud computing environment, outsourcing service mode of data storage causes the security problem, the reliability of data cannot be guaranteed, and the privacy preservation problem has aroused wide concern. In order to solve the problem of inefficiency and high-complexity caused by traditional privacy preservation methods such as data encryption and access control technology, a privacy preservation method based on data coloring is proposed. The data coloring model is established and the coloring mechanism is adopted to deal with the sensitive data of numerical attributes, and the cloud model similarity measurement based on arithmetic average least-approximability is adopted to authenticate the ownership of privacy data. On the premise of high availability of data, the method strengthens the security of the privacy information. Then, the performance, validity and the parameter errors of the algorithm are quantitatively analyzed by the experiments using the UCI dataset. Under the same conditions of privacy preservation requirements, the proposed method can track privacy leakage efficiently and reduce privacy leakage risks. Compared with the k-anonymity approach, the proposed method enhances the computational time efficiency by 18.5%.

The effects of coloring therapy on patients with generalized anxiety disorder

Generalized anxiety disorder(GAD)has harmful effects on physical and mental health and quality of life.Coloring therapy has been reported to have a positive effect on improving patient anxiety and depression.But there are no reported clinical trials examining their effectiveness as a treatment for GAD.This study was planned to evaluate the effectiveness of coloring therapy combined with conventional therapy in improving anxiety,depression,and positive and negative emotions with GAD.This randomized controlled study comprising 88 GAD patients was selected for intervention in different wards.The control group(n=45)was given conventional antianxiety medication and physical therapy,and the experimental group(n=43)received coloring therapy combined with conventional therapy.The Self-Rating Depression Scale,Self-Rating Anxiety Scale(SAS),Hamilton Depression Scale,Hamilton Anxiety Scale(HAMA),and Positive and Negative Affect Scale were assessed in both groups before and 3 weeks after the intervention.After the intervention,there were statistical differences in intra-and inter-group comparisons of anxiety,depression,and positive and negative mood scales in the experimental and control groups(p<.05).The minus in anxiety/positive emotions pre-and postintervention in the experimental group was statistically significant compared to that in anxiety/positive emotions pre-and postintervention in the control group(HAMA:d=1.45,95%confidence interval[CI](0.34,2.57),p=.011;SAS:d=3.87,95%CI(1.73,6.00),p=.001;positive:d=1.76,95%CI(0.17,3.34),p=.030).The minus in depressive/negative emotions pre-and postintervention in the experimental group was not statistically significant compared with that in depressive/negative emotions pre-and postintervention in the control group(p>.05).For GAD patients,adding coloring therapy based on conventional drug therapy and physical therapy can not only reduce depression and negative emotions but also have better effects on reducing anxiety and improving positive emotions than conventional therapy.

Adjacent vertex-distinguishing total colorings of K_s∨K_t

Let G be a simple graph and f be a proper total kcoloring of G. The color set of each vertex v of G is the set of colors appearing on v and the edges incident to v. The coloring f is said to be an adjacent vertex-distinguishing total coloring if the color sets of any two adjacent vertices are distinct. The minimum k for which such a coloring of G exists is called the adjacent vertex-distinguishing total chromatic number of G. The join graph of two vertex-disjoint graphs is the graph union of these two graphs together with all the edges that connect the vertices of one graph with the vertices of the other. The adjacent vertex-distinguishing total chromatic numbers of the join graphs of an empty graph of order s and a complete graph of order t are determined.

A DNA Computing Model for the Graph Vertex Coloring Problem Based on a Probe Graph

The biggest bottleneck in DNA computing is exponential explosion, in which the DNA molecules used as data in information processing grow exponentially with an increase of problem size. To overcome this bottleneck and improve the processing speed, we propose a DNA computing model to solve the graph vertex coloring problem. The main points of the model are as follows： The exponential explosion prob- lem is solved by dividing subgraphs, reducing the vertex colors without losing the solutions, and ordering the vertices in subgraphs; and the bio-operation times are reduced considerably by a designed parallel polymerase chain reaction （PCR） technology that dramatically improves the processing speed. In this arti- cle, a 3-colorable graph with 61 vertices is used to illustrate the capability of the DNA computing model. The experiment showed that not only are all the solutions of the graph found, but also more than 99% of false solutions are deleted when the initial solution space is constructed. The powerful computational capability of the model was based on specific reactions among the large number of nanoscale oligonu- cleotide strands. All these tiny strands are operated by DNA self-assembly and parallel PCR. After thou- sands of accurate PCR operations, the solutions were found by recognizing, splicing, and assembling. We also prove that the searching capability of this model is up to 0（3^59）. By means of an exhaustive search, it would take more than 896 000 years for an electronic computer （5 x 10^14 s-1） to achieve this enormous task. This searching capability is the largest among both the electronic and non-electronic computers that have been developed since the DNA computing model was proposed by Adleman＇s research group in 2002 （with a searching capability of 0（2^20））.