A proper [h]-total coloring c of a graph G is a proper total coloring c of G using colors of the set [h] ={1, 2,..., h}. Let w（u） denote the sum of the color on a vertex u and colors on all the edges incident to u. ...A proper [h]-total coloring c of a graph G is a proper total coloring c of G using colors of the set [h] ={1, 2,..., h}. Let w（u） denote the sum of the color on a vertex u and colors on all the edges incident to u. For each edge uv ∈ E（G）, if w（u） ≠ w（v）, then we say the coloring c distinguishes adjacent vertices by sum and call it a neighbor sum distinguishing [h]-total coloring of G. By tndi∑ （G）, we denote the smallest value h in such a coloring of G. In this paper, we obtain that G is a graph with at least two vertices, if mad（G） 〈 3, then tndi∑ （G） ≤k ＋ 2 where k = max{△（G）, 5}. It partially confirms the conjecture proposed by Pilgniak and Wolniak.展开更多
Let G be a graph and let its maxiraum degree and maximum average degree be denoted by △（G） and mad（G）, respectively. A neighbor sum distinguishing k-edge colorings of graph G is a proper k-edge coloring of graph ...Let G be a graph and let its maxiraum degree and maximum average degree be denoted by △（G） and mad（G）, respectively. A neighbor sum distinguishing k-edge colorings of graph G is a proper k-edge coloring of graph G such that, for any edge uv ∈ E（G）, the sum of colors assigned on incident edges of u is different from the sum of colors assigned on incident edges of v. The smallest value of k in such a coloring of G is denoted by X∑ （G）. Flandrin et al. proposed the following conjecture that X＇∑ （G） ≤△ （G） ＋ 2 for any connected graph with at least 3 vertices and G ≠ C5. In this paper, we prove that the conjecture holds for a normal graph with mad（G） 〈 37/12and △ （G）≥ 7.展开更多
An edge coloring total k-labeling is a labeling of the vertices and the edges of a graph G with labels {1,2,..., k} such that the weights of the edges define a proper edge coloring of G. Here the weight of an edge is ...An edge coloring total k-labeling is a labeling of the vertices and the edges of a graph G with labels {1,2,..., k} such that the weights of the edges define a proper edge coloring of G. Here the weight of an edge is the sum of its label and the labels of its two end vertices. This concept was introduce by Brandt et al. They defined Xt＇（G） to be the smallest integer k for which G has an edge coloring total k-labeling and proposed a question： Is there a constant K with X^t（G） ≤△（G）＋1/2 K for all graphs G of maximum degree A（G）？ In this paper, we give a positive answer for outerplanar graphs ≤△（G）＋1/2 by showing that X＇t（G） ≤△（G）＋1/2 for each outerplanar graph G with maximum degree A（G）.展开更多
本文将认知无线电(cognitive radio,CR)和图论引入差分跳频(differential frequency hopping,DFH)网络,提出基于IC着色和干扰温度模型的认知差分跳频多址(IC-ITMA)原理,用IC着色与干扰温度理论控制网内用户的发射行为,网内各发射机在接...本文将认知无线电(cognitive radio,CR)和图论引入差分跳频(differential frequency hopping,DFH)网络,提出基于IC着色和干扰温度模型的认知差分跳频多址(IC-ITMA)原理,用IC着色与干扰温度理论控制网内用户的发射行为,网内各发射机在接收机处产生的干扰温度正交.接收机根据测得的干扰温度来区分它们,使之达到区分预期信号和干扰信号的目的.仿真结果表明,该方法较传统差分跳频网络可以显著提高抗多址干扰性能.展开更多
The concept of aqueous computing is presented here, first in full generality,and afterward, using an implementation in a specific enzymatic technology. Aqueous computing arosein the context of biomolecular (DNA) compu...The concept of aqueous computing is presented here, first in full generality,and afterward, using an implementation in a specific enzymatic technology. Aqueous computing arosein the context of biomolecular (DNA) computing, but the concept is independent of the specifics ofits biochemical origin. Alternate technologies for realizing aqueous computing are being consideredfor future implementation. A solution of an instance of the Boolean satisfiability problem, (SAT),is reported here that provides a new example of an aqueous computation that has been carried outsuccessfully. This small instance of the SAT problem is sufficiently complex to allow our currentenzymatic technology to be illustrated in detail. The reader is invited to participate in the richinterdisciplinary activity required by wet lab computing. A project is suggested to the reader fordetermining the three-colorings of a graph. The basic operations required for this project areexhibited in the solution of the SAT example reported here.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11161035)the Research Fund for the Doctoral Program of Shandong Jiaotong University+2 种基金supported by National Natural Science Foundation of China(Grant No.11101243)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20100131120017)the Scientific Research Foundation for the Excellent Middle-Aged and Youth Scientists of Shandong Province of China(Grant No.BS2012SF016)
文摘A proper [h]-total coloring c of a graph G is a proper total coloring c of G using colors of the set [h] ={1, 2,..., h}. Let w（u） denote the sum of the color on a vertex u and colors on all the edges incident to u. For each edge uv ∈ E（G）, if w（u） ≠ w（v）, then we say the coloring c distinguishes adjacent vertices by sum and call it a neighbor sum distinguishing [h]-total coloring of G. By tndi∑ （G）, we denote the smallest value h in such a coloring of G. In this paper, we obtain that G is a graph with at least two vertices, if mad（G） 〈 3, then tndi∑ （G） ≤k ＋ 2 where k = max{△（G）, 5}. It partially confirms the conjecture proposed by Pilgniak and Wolniak.
基金supported by the National Natural Science Foundation of China(Grant No.11571258)the National Natural Science Foundation of Shandong Province(Grant No.ZR2016AM01)Scientific Research Foundation of University of Jinan(Grant Nos.XKY1414 and XKY1613)
文摘Let G be a graph and let its maxiraum degree and maximum average degree be denoted by △（G） and mad（G）, respectively. A neighbor sum distinguishing k-edge colorings of graph G is a proper k-edge coloring of graph G such that, for any edge uv ∈ E（G）, the sum of colors assigned on incident edges of u is different from the sum of colors assigned on incident edges of v. The smallest value of k in such a coloring of G is denoted by X∑ （G）. Flandrin et al. proposed the following conjecture that X＇∑ （G） ≤△ （G） ＋ 2 for any connected graph with at least 3 vertices and G ≠ C5. In this paper, we prove that the conjecture holds for a normal graph with mad（G） 〈 37/12and △ （G）≥ 7.
基金Supported by National Natural Science Foundation of China(Grant Nos.61070230 and 11101243)Doctoral Fund of Ministry of Education of China(Grant No.20100131120017)the Scientific Research Foundation for the Excellent Middle-Aged and Young Scientists of Shandong Province(Grant No.BS2012SF016)
文摘An edge coloring total k-labeling is a labeling of the vertices and the edges of a graph G with labels {1,2,..., k} such that the weights of the edges define a proper edge coloring of G. Here the weight of an edge is the sum of its label and the labels of its two end vertices. This concept was introduce by Brandt et al. They defined Xt＇（G） to be the smallest integer k for which G has an edge coloring total k-labeling and proposed a question： Is there a constant K with X^t（G） ≤△（G）＋1/2 K for all graphs G of maximum degree A（G）？ In this paper, we give a positive answer for outerplanar graphs ≤△（G）＋1/2 by showing that X＇t（G） ≤△（G）＋1/2 for each outerplanar graph G with maximum degree A（G）.
文摘本文将认知无线电(cognitive radio,CR)和图论引入差分跳频(differential frequency hopping,DFH)网络,提出基于IC着色和干扰温度模型的认知差分跳频多址(IC-ITMA)原理,用IC着色与干扰温度理论控制网内用户的发射行为,网内各发射机在接收机处产生的干扰温度正交.接收机根据测得的干扰温度来区分它们,使之达到区分预期信号和干扰信号的目的.仿真结果表明,该方法较传统差分跳频网络可以显著提高抗多址干扰性能.
基金国家自然科学基金，the Leiden Center for Natural Computing, and the Leiden Institute for Advanced Computer Science
文摘The concept of aqueous computing is presented here, first in full generality,and afterward, using an implementation in a specific enzymatic technology. Aqueous computing arosein the context of biomolecular (DNA) computing, but the concept is independent of the specifics ofits biochemical origin. Alternate technologies for realizing aqueous computing are being consideredfor future implementation. A solution of an instance of the Boolean satisfiability problem, (SAT),is reported here that provides a new example of an aqueous computation that has been carried outsuccessfully. This small instance of the SAT problem is sufficiently complex to allow our currentenzymatic technology to be illustrated in detail. The reader is invited to participate in the richinterdisciplinary activity required by wet lab computing. A project is suggested to the reader fordetermining the three-colorings of a graph. The basic operations required for this project areexhibited in the solution of the SAT example reported here.
