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Group Connectivity and Group Colorings of Graphs -- A Survey

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Acta Mathematica Sinica,English Series 2011年第3期27卷 405-434页

作者： hong-jian lai Xiangwen LI Yehong SHAO Mingquan ZHAN College of Mathematics and System Sciences Xinjiang University Urumqi 830046 P. R. China Department of Mathematics West Virginia University Morgantown WV26506 USA Department of Mathematics Huazhong Normal University Wuhan 430070 P. R. China Department of Mathematics Ohio University Southern Campus Ironton OH 45638 USA Department of Mathematics Millersville University of Pennsylvania Millersville PA 17551 USA

In 1950s, Tutte introduced the theory of nowhere-zero flows as a tool to investigate the coloring problem of maps, together with his most fascinating conjectures on nowhere-zero flows. These have been extended by Jaeger et al. in 1992 to group connectivity, the nonhomogeneous form of nowhere-zero flows. Let G be a 2-edge-connected undirected graph, A be an （additive） abelian group and A＊ = A - {0}. The graph G is A-connected if G has an orientation D（G） such that for every map b ： V（G） → A satisfying ∑v∈V（G）b（v）： 0, there is a function f ： E（G） → A＊ such that for each vertex v ∈ V（G）, the total amount of f-values on the edges directed out from v minus the total amount of f-values on the edges directed into v is equal to b（v）. The group coloring of a graph arises from the dual concept of group connectivity. There have been lots of investigations on these subjects. This survey provides a summary of researches on group connectivity and group colorings of graphs. It contains the following sections. 1. Nowhere-zero Flows and Group Connectivity of Graphs 2. Complete Families and A-reductions 3. Reductions with Edge-deletions, Vertex-deletions and Vertex-splitting 4. Group Colorings as a Dual Concept of Group Connectivity 5. Brooks Theorem, Its Variations and Dual Forms 6. Planar Graphs 7. Group Connectivity of Graphs 7.1 Highly Connected Graphs and Collapsible Graphs 7.2 Degrees Conditions 7.3 Complementary Graphs 7.4 Products of Graphs 7.5 Graphs with Diameter at Most 2 7.6 Line Graphs and Claw-Free Graphs 7.7 Triangular Graphs 7.8 Claw-decompositions and All Tutte-orientations

关键词： Group connectivity group connectivity number group coloring group chromatic number

Supereulerian Graphs and the Petersen Graph

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Acta Mathematica Sinica,English Series 2014年第2期30卷 291-304页

作者： Xiao Min LI Lan LEI hong-jian lai Meng ZHANG Department of Mathematics and Statistics Chongqing Technology and Business University Department of Mathematics West Virginia University College of Mathematics and System Sciences Xinjiang University

A graphG is supereulerian if G has a spanning eulerian *** et al.[*** Theory,1,79–84（1977）]proposed the problem of characterizing supereulerian *** this paper,we prove that any 3-edge-connected graph with at most 11 edge-cuts of size 3 is supereulerian if and only if it cannot be contractible to the Petersen *** extends a former result of Catlin and lai[***,Ser.B,66,123–139（1996）].

关键词： Supereulerian graphs petersen graph edge-cut reduction contraction

On the Sizes of k-edge-maximal r-uniform Hypergraphs

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Acta Mathematicae Applicatae Sinica 2022年第3期38卷 532-539页

作者： Ying-zhi TIAN hong-jian lai Ji-xiang MENG Li-qiong XU College of Mathematics and System Sciences Xinjiang UniversityUrumqi 830046China Department of Mathematics West Virginia UniversityMorgantownWV 26506USA School of Science Jimei UniversityXiamen 361021China

Let H=(V,E)be a hypergraph,where V is a set of vertices and E is a set of non-empty subsets of V called *** all edges of H have the same cardinality r,then H is an r-uniform hypergraph;if E consists of all r-subsets of V,then H is a complete r-uniform hypergraph,denoted by K_(n)^(r),where n=|V|.A hypergraph H′=(V′,E′)is called a subhypergraph of H=(V,E)if V′⊆V and E′⊆*** edge-connectivity of a hypergraph H is the cardinality of a minimum edge set F⊆E such that H−F is not connected,where H−F=(V,E\F).An r-uniform hypergraph H=(V,E)is k-edge-maximal if every subhypergraph of H has edge-connectivity at most k,but for any edge e∈E(K_(n)^(r))\E(H),H+e contains at least one subhypergraph with edge-connectivity at least k+*** k and r be integers with k≥2 and r≥2,and let t=t(k,r)be the largest integer such that(t−1 r−1)≤*** is,t is the integer satisfying(t−1 r−1)≤k<(t r−1).We prove that if H is an r-uniform k-edge-maximal hypergraph such that n=|V(H)|≥t,then(i)|E(H)|≤(t r)+(n−t)k,and this bound is best possible;(ii)|E(H)|≥(n−1)k−((t−1)k−(t r))[n/t],and this bound is best possible.

关键词： Edge-connectivity k-edge-maximal hypergraphs r-uniform hypergraphs

Multigraphic Degree Sequences and Hamiltonian-connected Line Graphs

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Acta Mathematicae Applicatae Sinica 2021年第4期37卷 800-806页

作者： Ren-sen MA Ai-mei YU Ke-ke WANG hong-jian lai Department of Mathematics Beijing Jiaotong UniversityBeijing100044China Department of Mathematics Embry-Riddle Aeronautical UniversityPrescottAZUSA Department of Mathematics West Virginia UniversityMorgantownWVUSA

Let G be a *** that e=u1v1 and e′=u2v2 are two edges of *** e≠e′,then G(e,e′)is the graph obtained from G by replacing e=u1v1 with a path u1vev1 and by replacing e′=u2v2 with a path u2ve′v2,where ve,ve′are two new vertices not in V(G).If e=e′,then G(e,e′),also denoted by G(e),is obtained from G by replacing e=u1v1 with a path u1vev1.A graph G is strongly spanning trailable if for any e,e′∈E(G),G(e,e′)has a spanning(ve,ve′)-*** design of n processor network with given number of connections from each processor and with a desirable strength of the network can be modelled as a degree sequence realization problem with certain desirable graphical properties.A sequence d=(d1,d2,⋯,dn)is multigraphic if there is a multigraph G with degree sequence d,and such a graph G is called a realization of d.A multigraphic degree sequence d is strongly spanning trailable if d has a realization G which is a strongly spanning trailable graph,and d is line-hamiltonian-connected if d has a realization G such that the line graph of G is *** this paper,we prove that a nonincreasing multigraphic sequence d=(d1,d2)⋯,dn)is strongly spanning trailable if and only if either n=1 and d1=0 or n≥2 and dn≥*** this result,we prove that for a nonincreasing multigraphic sequence d=(d1,d2,⋯,dn),if n≥2 and dn≥3,then d is line-hamiltonian-connected.

关键词： strongly spanning trailable graphs multigraphic degree sequence hamiltonian-connected graphs line graph

Progress and prospects of graphene-based materials in lithium batteries

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Rare Metals 2024年第5期43卷 1886-1905页

作者： Shen lai Tao Huang Pei Liu hong-Bin Wang Shi-Chun Yang Xin-Hua Liu Kai Yang Qian-Ling Zhang jian-hong Liu jiang-Tao Hu Graphene Composite Research Center College of Chemistry and Environmental EngineeringShenzhen UniversityShenzhen 518060China College of Physics and Optoelectronic Engineering Shenzhen UniversityShenzhen 518060China Shenzhen Eigen-Equation Graphene Technology Co.Ltd Shenzhen518060China School of Transportation Science and Engineering Beihang UniversityBeijing 100191China Department of Electrical and Electronic Engineering Advanced Technology InstituteUniversity of SurreyGuildfordSurrey GU27XHUK

Reasonable design and applications of graphene-based materials are supposed to be promising ways to tackle many fundamental problems emerging in lithium batteries,including suppression of electrode/electrolyte side reactions,stabilization of electrode architecture,and improvement of conductive ***,extensive fundamental research on this aspect has been performed so ***,when it comes to large-scale industrial applications,the utilization of graphene-based materials progresses at a very slow ***,there presents a severe technological decoupling between academic research and industrial application,and there is an urgent need to link ***,in order to address current issues of graphene-based materials used in lithium batteries,we present their latest advancements with stateof-the-art *** applications of graphenebased materials in practical lithium batteries are highlighted and predicted to bridge the gap between the academic progress and industrial manufacture,thereby paving the way for accelerating the development of graphenebased material as well as lithium battery industry.

关键词： Lithium batteries Graphene-based materials Academic research Industrial application Development direction

Reinforcing a Matroid to Have k Disjoint Bases

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Applied Mathematics 2010年第3期1卷 244-249页

作者： hong-jian lai Ping Li Yanting Liang Jinquan Xu 不详

Let denote the maximum number of disjoint bases in a matroid . For a connected graph , let , where is the cycle matroid of . The well-known spanning tree packing theorem of Nash-Williams and Tutte characterizes graphs with . Edmonds generalizes this theorem to matroids. In [1] and [2], for a matroid with , elements with the property that have been characterized in terms of matroid invariants such as strength and -partitions. In this paper, we consider matroids with , and determine the minimum of , where is a matroid that contains as a restriction with both and . This minimum is expressed as a function of certain invariants of , as well as a min-max formula. These are applied to imply former results of Haas [3] and of Liu et al. [4].

关键词： Disjoint Bases Edge-Disjoint Spanning Trees Spanning Tree Packing Numbers Strength

On a Class of Supereulerian Digraphs

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Applied Mathematics 2016年第3期7卷 320-326页

作者： Khalid A. Alsatami Xindong Zhang Juan Liu hong-jian lai Department of Mathematics College of Science Qassim University Buraydah KSA College of Mathematics Sciences Xinjiang Normal University Urumqi China Department of Mathematics West Virginia University Morgantown WV USA

The 2-sum of two digraphs and , denoted , is the digraph obtained from the disjoint union of and by identifying an arc in with an arc in . A digraph D is supereulerian if D contains a spanning eulerian subdigraph. It has been noted that the 2-sum of two supereulerian (or even hamiltonian) digraphs may not be supereulerian. We obtain several sufficient conditions on and for to be supereulerian. In particular, we show that if and are symmetrically connected or partially symmetric, then is supereulerian.

关键词： Supereulerian Digraph 2-Sums Arc-Strong-Connectivity Hamiltonian-Connected Digraphs

Research on the solid particle erosion wear of pipe steel for hydraulic fracturing based on experiments and numerical simulations

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Petroleum Science 2024年第4期21卷 2779-2792页

作者： Si-Qi Yang jian-Chun Fan Ming-Tao Liu De-Ning Li Jun-Liang Li Li-hong Han jian-Jun Wang Shang-Yu Yang Si-Wei Dai lai-Bin Zhang State Key Laboratory of Oil and Gas Equipment CNPC Tubular Goods Research Institute Key Laboratory of Oil and Gas Safety and Emergency Technology China University of Petroleum Oil Production Technology Research Institute of Liaohe Oilfield Company Tianjin Gas Storage Branch PetroChina Dagang Oilfield Company Petroleum Production Engineering Research Institute Daqing Oilfield Company

Erosion wear is a common failure mode in the oil and gas industry. In the hydraulic fracturing, the fracturing pipes are not only in high-pressure working environment, but also suffer from the impact of the high-speed solid particles in the fracturing fluid. Beneath such complex conditions, the vulnerable components of the pipe system are prone to perforation or even burst accidents, which has become one of the most serious risks at the fracturing site. Unfortunately, it is not yet fully understood the erosion mechanism of pipe steel for hydraulic fracturing. Therefore, this article provides a detailed analysis of the erosion behavior of fracturing pipes under complex working conditions based on experiments and numerical simulations. Firstly, we conducted erosion experiments on AISI 4135 steel for fracturing pipes to investigate the erosion characteristics of the material. The effects of impact angle, flow velocity and applied stress on erosion wear were comprehensively considered. Then a particle impact dynamic model of erosion wear was developed based on the experimental parameters, and the evolution process of particle erosion under different impact angles, impact velocities and applied stress was analyzed. By combining the erosion characteristics, the micro-structure of the eroded area, and the micro-mechanics of erosion damage, the erosion mechanism of pipe steel under fracturing conditions was studied in detail for the first time. Under high-pressure operating conditions, it was demonstrated through experiments and numerical simulations that the size of the micro-defects in the eroded area increased as the applied stress increased, resulting in more severe erosion wear of fracturing pipes.

关键词： Erosion wear Applied stress Particle impact dynamics Erosion mechanism

Clinical characteristics of patients with early gastric prematurity cancer and analysis of complications by endoscopic resection

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World Journal of Gastrointestinal Oncology 2024年第9期16卷 3898-3904页

作者： hong Zhao Xiang-Yu Shi Li-Li Lv Yan-Zong lai Xiao-Xiao Bao jian-Wen Hu Department of Gastroenterology Dongyang People’s HospitalDongyang 322100Zhejiang ProvinceChina Department of Gastroenterology Yiwu Tianxiang Medical East HospitalYiwu 322100Zhejiang ProvinceChina Department of Pathology Dongyang People’s HospitalDongyang 322100Zhejiang ProvinceChina

BACKGROUND Gastric cancer,a prevalent malignancy,poses a severe threat to the health of residents in *** intervention in early stages can extend patients’*** To analyze clinical characteristics of patients with early gastric cancer and efficacy and risk of complications associated with endoscopic *** This study included 175 patients with early gastric cancer treated at our hospital,with no restrictions on sex or *** data,pathological information,and endoscopic biopsy results were *** clinical characteristics of early gastric cancer were analyzed,and endoscopic resection was *** efficacy and incidence of complications were *** analysis was performed using SPSS 26.0 and GraphPad Prism 8.0 *** A total of 175 patients with early gastric cancer were included,with 75.43%(n=132)males and 24.57%(n=43)females.38.29%(n=67)and 35.43%(n=62)of patients had a history of smoking and alcohol consumption,*** included diabetes(8.57%,n=15),coronary heart disease(10.29%,n=18),and hypertension(43.43%,n=76),which was highly prevalent.A history of abdominal surgery and family history of digestive system cancer accounted for 21.14%and 17.14%,*** most common lesion location was the antral part of the stomach(52.00%,n=91),followed by the gastric angle,body,and *** pathological types were predominantly high-grade intraepithelial neoplasia(28.00%,n=49)and well-differentiated adenocarcinoma(26.86%,n=47),followed by moderately differentiated adenocarcinoma,high-moderately differentiated adenocarcinoma,and moderate-lowly differentiated adenocarcinoma.89.14%of the patients had intestinal metaplasia and 85.14%had *** endoscopic resection,re-examination revealed that 13 patients had cancer cells at the tissue margin,with a positive margin rate of 7.43%.Postoperative complications included no cases of gastrointestinal obstruction,but incisional infec

关键词： Early gastric cancer Clinical characteristics Endoscopic resection Complications