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Perfect 1-k Matchings of Bipartite Graphs
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作者 Wenduan Dai Yan Liu Yanfang Wu 《Open Journal of Discrete Mathematics》 2024年第4期43-53,共11页
Let k be a positive integer and G a bipartite graph with bipartition (X,Y). A perfect 1-k matching is an edge subset M of G such that each vertex in Y is incident with exactly one edge in M and each vertex in X is inc... Let k be a positive integer and G a bipartite graph with bipartition (X,Y). A perfect 1-k matching is an edge subset M of G such that each vertex in Y is incident with exactly one edge in M and each vertex in X is incident with exactly k edges in M. A perfect 1-k matching is an optimal semi-matching related to the load-balancing problem, where a semi-matching is an edge subset M such that each vertex in Y is incident with exactly one edge in M, and a vertex in X can be incident with an arbitrary number of edges in M. In this paper, we give three sufficient and necessary conditions for the existence of perfect 1-k matchings and for the existence of 1-k matchings covering | X |−dvertices in X, respectively, and characterize k-elementary bipartite graph which is a graph such that the subgraph induced by all k-allowed edges is connected, where an edge is k-allowed if it is contained in a perfect 1-k matching. 展开更多
关键词 Bipartite graph Semi-Matching Perfect 1-k Matching k-Elementary graph
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Markov Chains Based on Random Generalized 1-Flipper Operations for Connected Regular Multi-digraphs
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作者 邓爱平 伍陈晨 +1 位作者 王枫杰 胡宇庭 《Journal of Donghua University(English Edition)》 CAS 2023年第1期110-115,共6页
The properties of generalized flip Markov chains on connected regular digraphs are discussed.The 1-Flipper operation on Markov chains for undirected graphs is generalized to that for multi-digraphs.The generalized 1-F... The properties of generalized flip Markov chains on connected regular digraphs are discussed.The 1-Flipper operation on Markov chains for undirected graphs is generalized to that for multi-digraphs.The generalized 1-Flipper operation preserves the regularity and weak connectivity of multi-digraphs.The generalized 1-Flipper operation is proved to be symmetric.Moreover,it is presented that a series of random generalized 1-Flipper operations eventually lead to a uniform probability distribution over all connected d-regular multi-digraphs without loops. 展开更多
关键词 random graph transformation regular multi-digraph Markov chain 1-Flipper triangle reverse
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血清Nrf2、Keap1水平变化与糖尿病视网膜病变分期间关系 被引量:1
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作者 范存莉 徐维诚 +1 位作者 陈玮 翁月胜 《徐州医科大学学报》 CAS 2024年第1期37-42,共6页
目的探讨血清单核细胞核因子E2相关因子(Nrf2)、Kelch样ECH关联蛋白1(Keap1)水平变化与糖尿病视网膜病变(DR)分期间关系。方法选取2020年4月—2023年2月如皋市中医院DR患者147例作为观察组,并根据DR分期分为非增生型糖尿病视网膜病变(NP... 目的探讨血清单核细胞核因子E2相关因子(Nrf2)、Kelch样ECH关联蛋白1(Keap1)水平变化与糖尿病视网膜病变(DR)分期间关系。方法选取2020年4月—2023年2月如皋市中医院DR患者147例作为观察组,并根据DR分期分为非增生型糖尿病视网膜病变(NPDR)、增生型糖尿病视网膜病变(PDR);另选取同期糖尿病无视网膜病变患者49例作为对照Ⅰ组,健康体检者49例作为对照Ⅱ组。对比3组及观察组不同DR分期患者血清Nrf2、Keap1水平,Spearman秩相关系数分析血清Nrf2、Keap1水平与DR分期间关系;多因素logistic回归分析血清Nrf2、Keap1水平对DR分期的影响;限制性立方样条图分析血清Nrf2、Keap1水平与DR分期的剂量-效应关系。结果观察组血清Nrf2水平低于对照Ⅰ组、对照Ⅱ组,Keap1水平高于对照Ⅰ组、对照Ⅱ组,对照Ⅰ组血清Nrf2水平低于对照Ⅱ组,Keap1水平高于对照Ⅱ组(P<0.05);随DR分期增加,血清Nrf2水平呈降低趋势,血清Keap1水平呈升高趋势(P<0.05);血清Nrf2水平与DR分期呈负相关(r=-0.806,P<0.001),血清Keap1水平与DR分期呈正相关(r=0.854,P<0.001);经多因素logistic回归分析,高血压、糖尿病发病年龄、总胆固醇对DR分期无显著影响(P>0.05),血清Nrf2水平是DR分期的独立保护因素,高脂血症、糖尿病病程、空腹血糖、糖化血红蛋白、血清Keap1水平是DR分期的独立危险因素(P<0.05);限制性立方样条图分析显示,血清Nrf2(χ^(2)=11.800,P<0.001)、Keap1(χ^(2)=8.401,P=0.015)水平与DR分期间存在非线性关系,控制其他病变为固定变量,血清Nrf2水平<1.70μg/L、血清Keap1水平>3.00μg/L时,PDR风险显著增加。结论血清Nrf2、Keap1水平变化与DR分期关系密切,血清Nrf2水平<1.70μg/L、血清Keap1水平>3.00μg/L时提示DR进展至PDR的风险显著增加。 展开更多
关键词 糖尿病视网膜病变 单核细胞核因子E2相关因子 Kelch样ECH关联蛋白1 增生型糖尿病视网膜病变 限制性立方样条图
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K_(1,k)-FACTORIZATION OF BIPARTITE GRAPHS 被引量:2
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作者 DU BEILIANG 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1997年第4期121-126,共6页
In this paper, a necessary condition for a bipartite graph λK m,n to be K 1,k factorizable and a sufficient condition for kK m,n to have a K 1,k factorization whenever k is a prime numbe... In this paper, a necessary condition for a bipartite graph λK m,n to be K 1,k factorizable and a sufficient condition for kK m,n to have a K 1,k factorization whenever k is a prime number are given. 展开更多
关键词 Bipartite graph K1 k-factor K1 k-factorization
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FRACTIONAL (g, f)-FACTORS OF GRAPHS 被引量:7
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作者 刘桂真 张兰菊 《Acta Mathematica Scientia》 SCIE CSCD 2001年第4期541-545,共5页
This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be i... This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be induced. 展开更多
关键词 fractional (g f)-factor augmenting path graph
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ORTHOGONAL (g,f)-FACTORIZAFIONS OF BIPARTITE GRAPHS 被引量:3
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作者 刘桂真 董鹤年 《Acta Mathematica Scientia》 SCIE CSCD 2001年第3期316-322,共7页
Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two positive integer-valued functions defined on V(G) such that g(x) ≤ f(x) for every vertex x of V(G). Then a (g, f)-factor of G ... Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two positive integer-valued functions defined on V(G) such that g(x) ≤ f(x) for every vertex x of V(G). Then a (g, f)-factor of G is a spanning subgraph H of G such that g(x) ≤ dH(x) 5 f(x) for each x ∈ V(H). A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {F1, F2,…… , Fm } and H be a factorization and a subgraph of G, respectively. If F, 1 ≤ i ≤ m, has exactly one edge in common with H, then it is said that ■ is orthogonal to H. It is proved that every bipartite (mg + m - 1, mf - m + 1 )-graph G has a (g, f)-factorization orthogonal to k vertex disjoint m-subgraphs of G if 2-k ≤ g(x) for all x ∈ V(G). Furthermore, it is showed that the results in this paper are best possible. 展开更多
关键词 Bipartite graph (g f)-factor orthogonal factorization
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Bondage Number of 1-Planar Graph 被引量:1
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作者 Qiaoling Ma Sumei Zhang Jihui Wang 《Applied Mathematics》 2010年第2期101-103,共3页
The bondage number of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph a domination number greater than the domination number of G. In this paper, we prove that ... The bondage number of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph a domination number greater than the domination number of G. In this paper, we prove that for a 1-planar graph G. 展开更多
关键词 DOMINATION NUMBER Bondage NUMBER 1-Planar graph Combinatorial PROBLEM
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<i>L</i>(0, 1)-Labelling of Cactus Graphs 被引量:1
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作者 Nasreen Khan Madhumangal Pal Anita Pal 《Communications and Network》 2012年第1期18-29,共12页
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
关键词 graph Labelling Code ASSIGNMENT L(0 1)-Labelling CACTUS graph
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A Neighborhood Condition for Graphs to Have Special [a,b]-Factor
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作者 Jinguo Lei Qingzhi Yu +1 位作者 Changhua Huang Man Liu 《Applied Mathematics》 2014年第1期212-215,共4页
Let G be a graph of order n, and let a and b be integers, such that 1 ≤ a b. Let H be a subgraph of G with m(≤b) edges, and δ(G) be the minimum degree. We prove that G has a [a,b]-factor containing all edges of H i... Let G be a graph of order n, and let a and b be integers, such that 1 ≤ a b. Let H be a subgraph of G with m(≤b) edges, and δ(G) be the minimum degree. We prove that G has a [a,b]-factor containing all edges of H if , , and when a ≤ 2, . 展开更多
关键词 graph FACTOR [a b]-factor The Minimum DEGREE NEIGHBORHOOD CONDITION
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A Note on SK, SK<sub>1</sub>, SK<sub>2</sub>Indices of Interval Weighted Graphs
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作者 Semiha Başdaş Nurkahlı Şerife Büyükköse 《Advances in Linear Algebra & Matrix Theory》 2021年第1期14-20,共7页
In this study, the SK, SK<sub>1</sub> and SK<sub>2</sub> indices are defined on weighted graphs. Then, the SK, SK<sub>1</sub> and SK<sub>2</sub> indices are defined on i... In this study, the SK, SK<sub>1</sub> and SK<sub>2</sub> indices are defined on weighted graphs. Then, the SK, SK<sub>1</sub> and SK<sub>2</sub> indices are defined on interval weighted graphs. Their behaviors are investigated under some graph operations by using these definitions. 展开更多
关键词 SK Index SK1 Index SK2 Index Weighted graph Interval Weighted graph
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Intergenic subset organization within a set of geographically-defined viral sequences from the 2009 H1N1 influenza A pandemic
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作者 William A. Thompson Joel K. Weltman 《American Journal of Molecular Biology》 2012年第1期32-41,共10页
We report a bioinformatic analysis of the datasets of sequences of all ten genes from the 2009 H1N1 influenza A pandemic in the state of Wisconsin. The gene with the greatest summed information entropy was found to be... We report a bioinformatic analysis of the datasets of sequences of all ten genes from the 2009 H1N1 influenza A pandemic in the state of Wisconsin. The gene with the greatest summed information entropy was found to be the hemagglutinin (HA) gene. Based upon the viral ID identifier of the HA gene sequence, the sequences of all of the genes were sorted into two subsets, depending upon whether the nucleotide occupying the position of maximum entropy, position 658 of the HA sequence, was either A or U. It was found that the information entropy (H) distributions of subsets differed significantly from each other, from H distributions of randomly generated subsets and from the H distributions of the complete datasets of each gene. Mutual information (MI) values facilitated identification of nine nucleotide positions, distributed over seven of the influenza genes, at which the nucleotide subsets were disjoint, or almost disjoint. Nucleotide frequencies at these nine positions were used to compute mutual information values that subsequently served as weighting factors for edges in a graph net-work. Seven of the nucleotide positions in the graph network are sites of synonymous mutations. Three of these sites of synonymous mutation are within a single gene, the M1 gene, which occupied the position of greatest graph centrality. It is proposed that these bioinformatic and network graph results may reflect alterations in M1-mediated viral packaging and exteriorization, known to be susceptible to synonymous mutations. 展开更多
关键词 Influenza A H1N1 Bioinformatics Genes PANDEMIC Epidemic Information Entropy MutualInFormation graph Network CENTRALITY SUBSETS
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<i>L</i>(2,1)-Labeling of the Brick Product Graphs
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作者 Xiujun Zhang Hong Yang Hong Li 《Journal of Applied Mathematics and Physics》 2017年第8期1529-1536,共8页
A k-L(2,1)-labeling for a graph G is a function such that whenever and whenever u and v are at distance two apart. The λ-number for G, denoted by λ(G), is the minimum k over all k-L(2,1)-labelings of G. In this pape... A k-L(2,1)-labeling for a graph G is a function such that whenever and whenever u and v are at distance two apart. The λ-number for G, denoted by λ(G), is the minimum k over all k-L(2,1)-labelings of G. In this paper, we show that for or 11, which confirms Conjecture 6.1 stated in [X. Li, V. Mak-Hau, S. Zhou, The L(2,1)-labelling problem for cubic Cayley graphs on dihedral groups, J. Comb. Optim. (2013) 25: 716-736] in the case when or 11. Moreover, we show that? if 1) either (mod 6), m is odd, r = 3, or 2) (mod 3), m is even (mod 2), r = 0. 展开更多
关键词 graph LABELING BRICK Product graph L((2 1)-Labeling Frequency ASSIGNMENT Problem
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单一4-边形环己烷类分子图的l_(1)-嵌入性
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作者 熊志坤 王广富 《华东交通大学学报》 2023年第6期115-120,共6页
图的度量空间与l_(1)-空间的某个子空间同构的图称为l_(1)-嵌入的。单一4-边形环己烷类分子图是指嵌入到平面上恰有1个四边形面,其他都是六边形面,且内点度为3,边界点度为2或3的2连通平面图。证明了当4-边形上只有2个相邻3度点时,单一4... 图的度量空间与l_(1)-空间的某个子空间同构的图称为l_(1)-嵌入的。单一4-边形环己烷类分子图是指嵌入到平面上恰有1个四边形面,其他都是六边形面,且内点度为3,边界点度为2或3的2连通平面图。证明了当4-边形上只有2个相邻3度点时,单一4-边形环己烷类图是l_(1)-嵌入的,其他的都不是。 展开更多
关键词 环己烷类图 l_(1)-嵌入 l_(1)-图
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用秩1矩阵矫正法计算两类图的生成树数
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作者 雷玉娟 杨维玲 《厦门大学学报(自然科学版)》 CAS CSCD 北大核心 2023年第3期473-476,共4页
设P是完全二部图K_(m,n)的一个匹配,本文用秩1矩阵矫正法给出了完全二部图K_(m,n)中包含P中的所有边和不包含P中边的生成树数目公式的一个简单证明.
关键词 完全二部图 生成树 LAPLACIAN矩阵 1矩阵
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禁用{B_(k+1),K_(2,l+1)}的图α谱半径极值问题
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作者 周金秀 王文环 《青海师范大学学报(自然科学版)》 2023年第4期48-52,共5页
令K_(s,t)是完全二部图,K_(n)是完全图,其中s,t和n是正整数.令B_(4,l)是由l个共享一条边的K_(4)构成的图,B_(l)是由B_(4,l)的所有生成子图构成的集合.本文研究了禁用{B_(k+1),K_(2,l+1)}的图的最大α-谱半径问题.利用B_(k+1)和K_(2,l+1... 令K_(s,t)是完全二部图,K_(n)是完全图,其中s,t和n是正整数.令B_(4,l)是由l个共享一条边的K_(4)构成的图,B_(l)是由B_(4,l)的所有生成子图构成的集合.本文研究了禁用{B_(k+1),K_(2,l+1)}的图的最大α-谱半径问题.利用B_(k+1)和K_(2,l+1)的结构特点以及基本不等式,在具有n个顶点、最大度为Δ且禁用{B_(k+1),K_(2,l+1)}的连通图中,获得了α-谱半径的上界,且刻画了达到上界的极值图.相应地,在具有n个顶点、最大度为Δ且禁用B_(k+1)或K_(2,l+1)的连通图中,得到了α-谱半径的上界. 展开更多
关键词 α-谱半径 禁用{B_(k+1) K_(2 l+1)} 谱Turán型极值问题
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1-平面图的奇着色数最多是21
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作者 郭春强 吴宝音都仍 《新疆大学学报(自然科学版)(中英文)》 CAS 2023年第3期267-273,共7页
对于任何一个图G的正常点着色φ而言,如果对于任何一个非孤立点x,存在一个颜色c使得|φ^(-1)(c)∩N_(G)(x)|是奇的,则φ被称为图G的奇着色.如果一个图能画在一个平面上,使得每一边至多被另一条边相交,则这样的图被称为1-平面图.证明了... 对于任何一个图G的正常点着色φ而言,如果对于任何一个非孤立点x,存在一个颜色c使得|φ^(-1)(c)∩N_(G)(x)|是奇的,则φ被称为图G的奇着色.如果一个图能画在一个平面上,使得每一边至多被另一条边相交,则这样的图被称为1-平面图.证明了任何一个1-平面图是奇21-着色的,改进了最近由Cranston,Lafferty和Song得到的界23. 展开更多
关键词 正常着色 奇着色 1-平面图
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1∶2000基础数字线划图动态更新质检方法研究--以浙江省为例
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作者 吴为民 《测绘与空间地理信息》 2023年第3期116-119,共4页
分析了1∶2000基础数字线划图动态更新方法;分析了动态更新容易存在的问题,针对存在的问题提出了解决方法,进一步研究出新的抽样方式及样本质量评价方式,更加科学、合理地评价成果的质量,对其他比例尺基础数字线划图更新也可提供参照。
关键词 1∶2000基础数字线划图 动态更新 质检方法
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边色临界图的1-因子和几乎1-因子的存在性 被引量:2
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作者 苗连英 苗正科 +1 位作者 段滋明 曲积彬 《中国矿业大学学报》 EI CAS CSCD 北大核心 2008年第1期139-141,共3页
根据Vizing邻接引理和关于临界图的独立数的一个结论,利用图的1-因子和几乎1-因子存在的充要条件,采用结构图论的方法证明了:1)若G是2n阶Δ-临界图,且Δ≥n,δ≥n-2,则G存在1-因子;2)若G是2n+1阶Δ-临界图,且Δ≥n+1,δ≥n-2,则G存在几... 根据Vizing邻接引理和关于临界图的独立数的一个结论,利用图的1-因子和几乎1-因子存在的充要条件,采用结构图论的方法证明了:1)若G是2n阶Δ-临界图,且Δ≥n,δ≥n-2,则G存在1-因子;2)若G是2n+1阶Δ-临界图,且Δ≥n+1,δ≥n-2,则G存在几乎1-因子. 展开更多
关键词 1-因子 几乎1-因子 边色数 临界图 独立集
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Hamiltonian[k,k+1]-因子(英文) 被引量:5
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作者 蔡茂诚 方奇志 李延军 《数学进展》 CSCD 北大核心 2003年第6期722-726,共5页
本文考虑n/2-临界图中Hamiltonian[k,k+1]-因子的存在性。Hamiltonian[k,k+1]-因子是指包含Hamiltonian圈的[k,k+1]-因子;给定阶数为n的简单图G,若δ(G)≥n/2而δ(G\e)<n/2(对任意的e∈E(G)),则称G为n/2-临界图。设k为大于等于2的整... 本文考虑n/2-临界图中Hamiltonian[k,k+1]-因子的存在性。Hamiltonian[k,k+1]-因子是指包含Hamiltonian圈的[k,k+1]-因子;给定阶数为n的简单图G,若δ(G)≥n/2而δ(G\e)<n/2(对任意的e∈E(G)),则称G为n/2-临界图。设k为大于等于2的整数,G为n/2-临界图(其中n≥4k-6且n≥7),我们证明了对于G的任何Hamiltonian圈C,G中必存在包含C的[k,k+1]-因子。该结果改进了现有的一些有关Hamiltonian[k,k+1]-因子存在性的结果。 展开更多
关键词 n/2-临界图 Hamiltonian[k k+1]-因子 存在性 Hamiltonian圈 简单图
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1-平面图的线性荫度(英文) 被引量:8
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作者 张欣 刘桂真 吴建良 《运筹学学报》 CSCD 2011年第3期38-44,共7页
证明了最大度△≥33的1-平面图的线性荫度为[△/2]
关键词 1-平面图 1-嵌入图 线性荫度
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