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 x_(vt)^(ie)(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.

Adjacent Vertex-distinguishing E-total Coloring on Some Join Graphs Cm ∨ 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.

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.

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 χAa(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.

Adjacent Vertex Distinguishing I-total Coloring of Outerplanar Graphs

Let G be a simple graph with no isolated edge. An/-total coloring of a graphG is a mapping Ф ： V（G） U E（G） → （1, 2,…… , k） such that no adjacent vertices receive thesame color and no adjacent edges receive the same color. An/-total coloring of a graph G issaid to be adjacent vertex distinguishing if for any pair of adjacent vertices u and v of G, wehave CФ（u） ≠ CФ（v）, where CФ（u） denotes the set of colors of u and its incident edges. Theminimum number of colors required for an adjacent vertex distinguishing I-total coloring of GG is called the adjacent vertex distinguishing I-total chromatic number, denoted by Xat（G）.In this paper, we characterize the adjacent vertex distinguishing I-total chromatic numberof outerplanar graphs.

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 χ_(vt)~e(G) and is called the VDET chromatic number of G. The VDET coloring of complete bipartite graph K_(7,n)(7 ≤ n ≤ 95) is discussed in this paper and the VDET chromatic number of K_(7,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.

Distinguishing the Effects of Cryosphere Change in the Background of Climate Change in China

Climate change has major impacts directly on the natural ecosystem and human society, of which the cryosphere is most easily affected be-cause of its frangibility and sensitivity. Similarly, cryosphere change has numerous impacts on the natural ecosystem and human society, which may resemble an indirect influence of climate change. These two types of impacts, in shared fields, are distinguished in space and time by effective mechanisms and processes. Climate change has positive and negative impacts on some systems, which may be adjusted by cryosphere change. These indirect and direct impacts may be distinguished, and then correct policies and measures can be made against these changes.

A Distinguishing Method and Distribution Characteristics of Fog and Haze Days in Fuzhou

For data of atmospheric composition missing,fog and haze days were distinguished based on the standard of meteorological industry Observation and Forecasting Levels of Haze( QX /T113-2010) and four user-defined standards,and using data of surface meteorological factors in Fuzhou City,China from 2005 to 2011,temporal distributions of fog and haze days were analyzed respectively to provide methods for fog and haze forecast. The results showed that there were 28. 9 fog days and 89. 7 haze days per year in Fuzhou. Both fog and haze days were variable,and there might be a day difference of twice to thrice among the years. They were the most in 2007,and then decreased in recent years. Both fog and haze days were more in winter and spring,accounted for 94. 1% and 70. 1% respectively,while in summer and autumn,they only accounted for5. 9% and 29. 9% respectively. In a day,fog mainly occurred from night to early morning,while haze occurred mainly at about noon,which demonstrated that fog and haze are different synoptic phenomena. The mass concentration of PM2. 5in fog days was 34 μg /m3,while it was 61 μg/m3in haze days,and in 22% of haze days it was larger than 75 μg /m3,which was above the national second-grade ambient air quality standard.

The Application of Genetic Algorithms and Multidimensional Distinguishing Model in Forecasting and Evaluating Credits for Mobile Clients

To solve the arrearage problem that puzzled most of the mobile corporations, we propose an approach to forecast and evaluate the credits for mobile clients, devising a method that is of the coalescence of genetic algorithm and multidimensional distinguishing model. In the end of this pa-per, a result of a testing application in Zhuhai Branch, GMCC was provided. The precision of the forecasting and evaluation of the client's credit is near 90%. This study is very signifi-cant to the mobile communication corporation at all levels.The popularization of the techniques and the result would pro-duce great benefits of both society and economy.

Using Cohen’s Effect Size to Identify Distinguishing Statements in Q-Methodology

Q-methodology was introduced more than 80 years ago to study subjective topics such as attitudes, perceptions, preferences, and feelings and there has not been much change in its statistical components since then. In Q-methodology, subjective topics are studied using a combination of qualitative and quantitative techniques. It involves development of a sample of statements and rank-ordering these statements by study participants using a grid known as Q-sort table. After completion of Q-sort tables by the participants, a by-person factor analysis (i.e., the factor analysis is performed on persons, not variables or traits) is used to analyze the data. Therefore, each factor represents a group of individuals with similar views, feelings, or preferences about the topic of the study. Then, each group (factor) is usually described by a set of statements, called distinguishing statements, or statements with high or low factor scores. In this article, we review one important statistical issue, i.e. the criteria for identifying distinguishing statements and provide a review of its mathematical calculation and statistical background. We show that the current approach for identifying distinguishing statements has no sound basis, which may result in erroneous findings and seems to be appropriate only when there are repeated evaluations of Q-sample from the same subjects. However, most Q-studies include independent subjects with no repeated evaluation. Finally, a new approach is suggested for identifying distinguishing statements based on Cohen’s effect size. We demonstrate the application of this new formula by applying the current and the suggested methods on a Q-dataset and explain the differences.

Investigating the writing proficiency of pre-service English as a Second Language teachers:Making use of distinguishing features

This research aims to investigate the writing proficiency of Hong Kong pre-service ESL teachers,in particular how their writing proficiency differs as characterized by distinguishing features inherent in such teachers' writing performances. Over 120 pre-service ESL teachers from various programmes in local universities in Hong Kong were recruited for the study. Results showed that the higher their writing level,the better they performed in a set task as well as in grammatical range and accuracy. The different programmes they enrolled in could affect the number of cohesive devices they tended to use. Mode and years of study had an effect on task achievement and number of cohesive device. Pre-service teachers enrolled in the teacher training programmes on a part-time basis outperformed those enrolled on a full-time basis. Teachers with more teacher training outperformed newly admitted pre-service teachers.The results of this study could provide empirical evidence for identifying different levels of writing proficiency for Hong Kong pre-service ESL teachers. On this basis,the link between the writing proficiency of pre-service ESL teachers and their assessment of student scripts could be subsequently established in a follow-up study to explore their differences in scoring focuses and strategies when scoring students' writings. This could further contribute to teacher evaluation,teacher training concerning language proficiency,and the improvement of teachers' assessment literacy in high-stakes and L2 classroom writing assessment.

Neighbor Sum Distinguishing Index of Graphs with Maximum Average Degree

A proper k-edge coloring of a graph G = (V(G), E(G)) is an assignment c: E(G) → {1, 2, …, k} such that no two adjacent edges receive the same color. A neighbor sum distinguishing k-edge coloring of G is a proper k-edge coloring of G such that for each edge uv ∈ E(G). The neighbor sum distinguishing index of a graph G is the least integer k such that G has such a coloring, denoted by χ’Σ(G). Let be the maximum average degree of G. In this paper, we prove χ’Σ(G) ≤ max{9, Δ(G) +1} for any normal graph G with . Our approach is based on the discharging method and Combinatorial Nullstellensatz.

Deterministically distinguishing a remote Bell state

It has been proven that,with a single copy provided,the four Bell states cannot be distinguished by local operations and classical communications (LOCC).Traditionally,a Bell basis projective measurement is needed to distinguish the four Bell states,which is usually carried out with a local interference between two particles.This paper presents an interesting protocol that allows two remote parties to distinguish four Bell states deterministically.We prove that our protocol of distinguishing remote Bell states is beyond LOCC.

Completely Distinguishing Individual A-genome Chromosomes and Their Karyotyping Analysis by Multiple BAC-FISH

Multiple BAC-FISH is a powerful tool for modern cytogenetic researching in both animals and plants.But in cotton,this technique is unavailable due to the high percentage of repetitive sequences.

ON EQUITABLE VERTEX DISTINGUISHING EDGE COLORINGS OF TREES

It has been known that determining the exact value of vertex distinguishing edge index χ's (G) of a graph G is difficult, even for simple classes of graphs such as paths, cycles,bipartite complete graphs, complete, graphs, and graphs with maximum degree 2. Letnd(G)denote the number of vertices of degree d in G, and let χ'es (G) be the equitable vertexdistinguishing edge index of G. We show that a tree T holds n1(T ) ≤χ's (T ) ≤ n1 (T) + 1and χ's (T ) = χ'es (T ) if T satisfies one of the following conditions (i) n2(T) ≤ (T) or(ii) there exists a constant c with respect to 0 < c < 1 such that n2(T) ≤ cn1(T) and∑((3 ≤ d ≤△(T))nd(T) ≤ (1-c)n1(T) + 1.

Smarandachely Adjacent-vertex-distinguishing Proper Edge Coloring ofK4 ∨ Kn

Let f be a proper edge coloring of G using k colors.For each x∈V(G),the set of the colors appearing on the edges incident with x is denoted by S_f(x)or simply S(x)if no confusion arise.If S(u)■S(v)and S(v)■S(u)for any two adjacent vertices u and v,then f is called a Smarandachely adjacent vertex distinguishing proper edge coloring using k colors,or k-SA-edge coloring.The minimum number k for which G has a Smarandachely adjacent-vertex-distinguishing proper edge coloring using k colors is called the Smarandachely adjacent-vertex-distinguishing proper edge chromatic number,or SAedge chromatic number for short,and denoted byχ'_(sa)(G).In this paper,we have discussed the SA-edge chromatic number of K_4∨K_n.

Upper bounds on vertex distinguishing chromatic index of some Halin graphs

A vertex distinguishing edge coloring of a graph G is a proper edge coloring of G such that any pair of vertices has the distinct sets of colors. The minimum number of colors required for a vertex distinguishing edge coloring of a graph G is denoted by χ s′ (G). In this paper, we obtained upper bounds on the vertex distinguishing chromatic index of 3-regular Halin graphs and Halin graphs with △(G) ≥ 4, respectively.

Adjacent Vertex Distinguishing Total Coloring of M（Tn）

如果为任何东西二个邻近的顶点有不同颜色 sets.According 到树的性质， G 的 k 合适的全部的着色被称为邻近的区分，区分全部的色彩的数字的邻近的顶点将用方法为树的 Mycielski 图被决定感应。