Let G(V,E) be a simple graph and G^k be a k-power graph defined byV(G~*) = V(G), E(G^k) = E(G) ∪{uv|d(u,v) =k} for natural number k. In this paper,it is proved that P_n^3 is a graceful graph.
An L(0,1)-labelling of a graph G is an assignment of nonnegative integers to the vertices of G such that the difference between the labels assigned to any two adjacent vertices is at least zero and the difference betw...An L(0,1)-labelling of a graph G is an assignment of nonnegative integers to the vertices of G such that the difference between the labels assigned to any two adjacent vertices is at least zero and the difference between the labels assigned to any two vertices which are at distance two is at least one. The span of an L(0,1)-labelling is the maximum label number assigned to any vertex of G. The L(0,1)-labelling number of a graph G, denoted by λ0.1(G) is the least integer k such that G has an L(0,1)-labelling of span k. This labelling has an application to a computer code assignment problem. The task is to assign integer control codes to a network of computer stations with distance restrictions. A cactus graph is a connected graph in which every block is either an edge or a cycle. In this paper, we label the vertices of a cactus graph by L(0,1)-labelling and have shown that, △-1≤λ0.1(G)≤△ for a cactus graph, where △ is the degree of the graph G.展开更多
随着人工智能技术的迅猛发展,大语言模型(large language models,LLMs)在自然语言处理和各种知识应用中展现了强大的能力.研究了国内大语言模型在中小学学科知识图谱自动标注中的应用,重点以义务教育阶段道德与法治学科和高中数学学科...随着人工智能技术的迅猛发展,大语言模型(large language models,LLMs)在自然语言处理和各种知识应用中展现了强大的能力.研究了国内大语言模型在中小学学科知识图谱自动标注中的应用,重点以义务教育阶段道德与法治学科和高中数学学科为例进行分析和探讨.在教育领域,知识图谱的构建对于整理和系统化学科知识具有重要意义,然而传统的知识图谱构建方法在数据标注方面存在效率低、耗费大量人工成本等问题.研究旨在通过大语言模型来解决这些问题,从而提升知识图谱构建的自动化和智能化水平.基于国内大语言模型的现状,探讨了其在学科知识图谱自动标注中的应用,以道德与法治和数学学科为例,阐述了相关方法和实验结果.首先,探讨了研究背景和意义.接着,综述了国内大语言模型的发展现状和学科知识图谱的自动标注技术.在方法与模型部分,尝试探索一种基于国内大语言模型的自动标注方法,力图完善其在学科知识图谱上的应用.还探讨了学科知识图谱人工标注方法模型,以此作为对比,评估自动标注方法的实际效果.在实验与分析部分,通过在道德与法治和数学学科的自动标注实验和对其结果的分析,发现两个学科的知识图谱自动标注均取得了较高的准确率和效率,与人工标注结果进行了深入比较分析,得出了一系列有价值的结论,验证了所提出方法的有效性和准确性.最后,对未来的研究方向进行了展望.总体而言,研究为学科知识图谱的自动标注提供了一种新的思路和方法,有望推动相关领域的进一步发展.展开更多
This paper shows that, for every unit interval graph, there is a labelling which is simultaneously optimal for the following seven graph labelling problems: bandwidth, cyclic bandwidth, profile, fill-in, cutwidth, mod...This paper shows that, for every unit interval graph, there is a labelling which is simultaneously optimal for the following seven graph labelling problems: bandwidth, cyclic bandwidth, profile, fill-in, cutwidth, modified cutwidth, and bandwidth sum(linear arrangement).展开更多
This paper establishes some local optimal fill-in theorems of graphs. The fill-in number of composite graphs is studied. An application of the local optimal fill-in theorems of graphs is given.
Let G be an outerplanar graph with maximum degree △. Let χ（G^2） and A（G） denote the chromatic number of the square and the L（2, 1）-labelling number of G, respectively. In this paper we prove the following resu...Let G be an outerplanar graph with maximum degree △. Let χ（G^2） and A（G） denote the chromatic number of the square and the L（2, 1）-labelling number of G, respectively. In this paper we prove the following results： （1） χ（G^2） = 7 if △= 6; （2） λ（G） ≤ △ ＋5 if △ ≥ 4, and ）,（G）≤ 7 if △ = 3; and （3） there is an outerplanar graph G with △ = 4 such that ）λ（G） = 7. These improve some known results on the distance two labelling of outerplanar graphs.展开更多
An orthogonal double cover (ODC) of a graph H is a collection of subgraphs (pages) of H, so that they cover every edge of H twice and the intersection of any two of them contains exactly one edge. An ODC G of H is cyc...An orthogonal double cover (ODC) of a graph H is a collection of subgraphs (pages) of H, so that they cover every edge of H twice and the intersection of any two of them contains exactly one edge. An ODC G of H is cyclic (CODC) if the cyclic group of order is a subgroup of the automorphism group of G. In this paper, we introduce a general orthogonal labelling for CODC of circulant graphs and construct CODC by certain classes of graphs such as complete bipartite graph, the union of the co-cycles graph with a star, the center vertex of which, belongs to the co-cycles graph and graphs that are connected by a one vertex.展开更多
文摘Let G(V,E) be a simple graph and G^k be a k-power graph defined byV(G~*) = V(G), E(G^k) = E(G) ∪{uv|d(u,v) =k} for natural number k. In this paper,it is proved that P_n^3 is a graceful graph.
文摘An L(0,1)-labelling of a graph G is an assignment of nonnegative integers to the vertices of G such that the difference between the labels assigned to any two adjacent vertices is at least zero and the difference between the labels assigned to any two vertices which are at distance two is at least one. The span of an L(0,1)-labelling is the maximum label number assigned to any vertex of G. The L(0,1)-labelling number of a graph G, denoted by λ0.1(G) is the least integer k such that G has an L(0,1)-labelling of span k. This labelling has an application to a computer code assignment problem. The task is to assign integer control codes to a network of computer stations with distance restrictions. A cactus graph is a connected graph in which every block is either an edge or a cycle. In this paper, we label the vertices of a cactus graph by L(0,1)-labelling and have shown that, △-1≤λ0.1(G)≤△ for a cactus graph, where △ is the degree of the graph G.
文摘随着人工智能技术的迅猛发展,大语言模型(large language models,LLMs)在自然语言处理和各种知识应用中展现了强大的能力.研究了国内大语言模型在中小学学科知识图谱自动标注中的应用,重点以义务教育阶段道德与法治学科和高中数学学科为例进行分析和探讨.在教育领域,知识图谱的构建对于整理和系统化学科知识具有重要意义,然而传统的知识图谱构建方法在数据标注方面存在效率低、耗费大量人工成本等问题.研究旨在通过大语言模型来解决这些问题,从而提升知识图谱构建的自动化和智能化水平.基于国内大语言模型的现状,探讨了其在学科知识图谱自动标注中的应用,以道德与法治和数学学科为例,阐述了相关方法和实验结果.首先,探讨了研究背景和意义.接着,综述了国内大语言模型的发展现状和学科知识图谱的自动标注技术.在方法与模型部分,尝试探索一种基于国内大语言模型的自动标注方法,力图完善其在学科知识图谱上的应用.还探讨了学科知识图谱人工标注方法模型,以此作为对比,评估自动标注方法的实际效果.在实验与分析部分,通过在道德与法治和数学学科的自动标注实验和对其结果的分析,发现两个学科的知识图谱自动标注均取得了较高的准确率和效率,与人工标注结果进行了深入比较分析,得出了一系列有价值的结论,验证了所提出方法的有效性和准确性.最后,对未来的研究方向进行了展望.总体而言,研究为学科知识图谱的自动标注提供了一种新的思路和方法,有望推动相关领域的进一步发展.
文摘This paper shows that, for every unit interval graph, there is a labelling which is simultaneously optimal for the following seven graph labelling problems: bandwidth, cyclic bandwidth, profile, fill-in, cutwidth, modified cutwidth, and bandwidth sum(linear arrangement).
基金the National Natural Science Foundation of China
文摘This paper establishes some local optimal fill-in theorems of graphs. The fill-in number of composite graphs is studied. An application of the local optimal fill-in theorems of graphs is given.
基金Supported by the National Natural Science Foundation of China(No.10771197)
文摘Let G be an outerplanar graph with maximum degree △. Let χ（G^2） and A（G） denote the chromatic number of the square and the L（2, 1）-labelling number of G, respectively. In this paper we prove the following results： （1） χ（G^2） = 7 if △= 6; （2） λ（G） ≤ △ ＋5 if △ ≥ 4, and ）,（G）≤ 7 if △ = 3; and （3） there is an outerplanar graph G with △ = 4 such that ）λ（G） = 7. These improve some known results on the distance two labelling of outerplanar graphs.
文摘An orthogonal double cover (ODC) of a graph H is a collection of subgraphs (pages) of H, so that they cover every edge of H twice and the intersection of any two of them contains exactly one edge. An ODC G of H is cyclic (CODC) if the cyclic group of order is a subgroup of the automorphism group of G. In this paper, we introduce a general orthogonal labelling for CODC of circulant graphs and construct CODC by certain classes of graphs such as complete bipartite graph, the union of the co-cycles graph with a star, the center vertex of which, belongs to the co-cycles graph and graphs that are connected by a one vertex.
