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新疆大学学报（自然科学版）（中英文） 2024年第1期41卷 20-26,36页

作者：周恋恋刘康孟吉翔新疆大学数学与系统科学学院新疆乌鲁木齐830017

图的最小特征值作为刻画图结构性质的参数具有重要的研究意义,且相比于谱半径,图的最小特征值研究较少.在补图简单无向且连通的情况下,通过运用相关知识分析,在有n-4个悬挂点的n阶双圈图集中刻画了最小邻接特征值的下界.

关键词：补图双圈图最小特征值下界

Connectivities　of　Minimal　Cayley　Coset　Digraphs

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Applied Mathematics(A Journal of Chinese Universities) 1996年第4期11卷 497-500页

作者： meng jixiang Department of Mathematics Xinjiang University Urumqi

we prove that the Connectivities of Minimal Cayley Coset Digraphs are their regular degrees. Connectivity of transitive digraphs and a combinatorial propertyof finite groups Ann., Discrete Math., 8 1980 61--64 meng jixiang and Huang Qiongxiang On the connectivity of Cayley digraphs, to appear Sabidussi, G. Vertex transitive graphs Monatsh. Math., 68 1969 426--438 Watkins, M. E. Connectivity of transitive graphs J. Combin. Theory, 8 1970 23--29 Zemor, G. On positive and negative atoms of Cayley digraphs Discrete Applied Math., 23 1989 193--195 Department of Mathematics,Xinjiang University,Urumpi *** MATHEMATICS 3. Statement of Inexact Method Here we assume F to be continuousely differentiable. Inexact Newton method was first studied in the solution of smooth equations (see ). Now, such a technique has been widely used in optimizations, nonlinear complementarity problems and nonsmooth equations (see, and , etc.) In order to establish the related inexact methods,we introduce a nonlinear operator T(x): R n  R n . Its components are defined as follows: (T(x)p) i=[HL(2:1,Z;2,Z] (x k+p k) i, if i∈(x k), H i(x k)+ min {(p k) i,F i(x k) Tp k}, if i∈(x k), F i(x k)+F i(x k) Tp k, i∈(x k).(3.1) Then, it is clear that the subproblem (2.5) turns to T(x k)p k=0.(3.2) In inexact algorithm, we determine p k in the followinginexact way ( see ). ‖T(x k)p k‖ υ k‖H(x k)‖,(3.3) where υ k is a given positive sequence. It is then obviously that (3.2),or equivalently (2.5), is a special case of (3.3) corresponding to υ k=0 . In particular, (3.3) can be used as a termination rule of the iterative process for solving (2.5). The following proposition shows the existence of λ k satisfying (2.4). Proposition 3.1. Let F be continuously differe ntiable. υ k is chosen so that υ k  for some constant ∈(0,1). Then p k generated by (3.3) is a de

关键词： Connectivity Cayley coset digraph

EMBEDDINGS OF ONE KIND OF GRAPHS

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Applied Mathematics(A Journal of Chinese Universities) 1997年第3期12卷 253-258页

作者： meng jixiang AND HUANG QIONGXIANG Department of Mathematics Northern Jiatong University Beijing

In this paper, Hamiltonian cycles and decompositions of Cayley digraphs are investigated. Sufficient conditions are given for these two problems respectively. Furthermore, the conditions are also necessary for 2 regular Cayley digraphs. In addition, some known results about the Cartesian products of two directed cycles are also deduced.

关键词： Surface embedding graph

A survey on book-embedding of planar graphs

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Frontiers of Mathematics in China 2022年第2期17卷 255-273页

作者： Xiaxia GUAN Chuxiong WU Weihua YANG jixiang meng College of Mathematics Taiyuan University of TechnologyTaiyuan 030024China College of Mathematics and System Science Xinjiang UniversityUrumqi 830046China

The book-embedding problem arises in several area,such as very large scale integration(VLSI)design and routing multilayer printed circuit boards(PCBs).It can be used into various practical application fields.A book embedding of a graph G is an embedding of its vertices along the spine of a book,and an embedding of its edges to the pages such that edges embedded on the same page do not *** minimum number of pages in which a graph G can be embedded is called the pagenumber or book-thickness of the graph *** is an important measure of the quality for *** is NP-hard to research the pagenumber of book-embedding for a graph *** paper summarizes the studies on the book-embedding of planar graphs in recent years.

关键词： Book embedding planar graphs pagenumber

Embedding Generalized Petersen Graph in Books

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Chinese Annals of Mathematics,Series B 2016年第3期37卷 385-394页

作者： Bin ZHAO Wei XIONG Yingzhi TIAN jixiang meng College of Mathematics and System Science Xinjiang University

A book embedding of a graph G consists of placing the vertices of G on a spine and assigning edges of the graph to pages so that edges in the same page do not cross each other. The page number is a measure of the quality of a book embedding which is the minimum number of pages in which the graph G can be embedded. In this paper, the authors discuss the embedding of the generalized Petersen graph and determine that the page number of the generalized Petersen graph is three in some situations, which is best possible.

关键词： Book embedding Page number Generalized Petersen graph

Some Upper Bounds Related with Domination Number

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Journal of the Operations Research Society of China 2013年第2期1卷 217-225页

作者： Zhao Gu jixiang meng Zhao Zhang Jin E.Wan College of Mathematics and System Sciences Xin Jiang UniversityUrumqi 830046China College of Information Science and Engineering Xin Jiang UniversityUrumqi 830046China

For a simple and connected graph G,denote the domination number,the diameter,and the radius of G asβ(G),D(G),and r(G),*** this paper,we solve two conjectures on the upper bounds ofβ(G)·D(G)andβ(G)+r(G),which are p... 详细信息

关键词： AutoGraphiX Upper bounds Extremal tree Domination number

Almost all Cayley Graphs Are Hamiltonian

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Acta Mathematica Sinica,English Series 1996年第2期12卷 151-155页

作者： meng jixiang Huang Qiongxiang meng jixiang Huang Qiongxiang Department of Mathematics and Institute of Mathematics and Phisics Xinjiang University Urumqi,830046 China

It has been conjectured that there is a hamiltonian cycle in every finite connected Cayley *** spite of the difficulty in proving this conjecture,we show that almost all Cayley graphs are *** is,as the order n of a group G approaches infinity,the ratio of the number of hamiltonian Cayley graphs of G to the total number of Cayley graphs of G approaches 1.

关键词： Cay|ey graph Hamiltonian Random

A NOTE ON THE PAPER "ON THE CONNECTIVITY OF CAYLEY COLOR GRAPHS

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Systems Science and Mathematical Sciences 1995年第3期8卷 287-288页

作者： meng jixiang HUANG Qiongxiang(Department of Mathematics, Xiniiang University, Urumchi 830046, China)

ＡＮＯＴＥＯＮＴＨＥＰＡＰＥＲ＂ＯＮＴＨＥＣＯＮＮＥＣＴＩＶＩＴＹＯＦＣＡＹＬＥＹＣＯＬＯＲＧＲＡＰＨＳ＂￥ＭＥＮＧＪｉｘｉａｎｇ；ＨＵＡＮＧＱｉｏｎｇｘｉａｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｘｉ... 详细信息

ＡＮＯＴＥＯＮＴＨＥＰＡＰＥＲ＂ＯＮＴＨＥＣＯＮＮＥＣＴＩＶＩＴＹＯＦＣＡＹＬＥＹＣＯＬＯＲＧＲＡＰＨＳ＂￥ＭＥＮＧＪｉｘｉａｎｇ；ＨＵＡＮＧＱｉｏｎｇｘｉａｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉｎｉｉａｎｇＵｎｉｖｅｒｓｉｔｙ，...

关键词： Connectivity atom Cayley color graphs.

Super Cyclically Edge Connected Half Vertex Transitive Graphs

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Applied Mathematics 2013年第2期4卷 348-351页

作者： Haining Jiang jixiang meng Yingzhi Tian College of Mathematics and System Sciences Xinjiang University Urumqi China

Tian and meng in [Y. Tian and J. meng, λc -Optimally half vertex transitive graphs with regularity k, Information Processing Letters 109 (2009) 683 - 686] shown that a connected half vertex transitive graph with regularity k and girth g(G) ≥ 6 is cyclically optimal. In this paper, we show that a connected half vertex transitive graph G is super cyclically edge-connected if minimum degree δ(G) ≥ 6 and girth g(G) ≥ 6.

关键词： Cyclic Edge-Connectivity Cyclically Optimal Super Cyclically Edge-Connected Half Vertex Transitive Graph

Isomorphisms of Cayley Digraphs of Infinite Abelian Groups

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新疆大学学报(自然科学版)(中英文) 1996年第3期 17-21页

作者： meng jixiang (Department of Mathematics, Xinjiang University, Urumchi, 830046)

ＩｓｏｍｏｒｐｈｉｓｍｓｏｆＣａｙｌｅｙＤｉｇｒａｐｈｓｏｆＩｎｆｉｎｉｔｅＡｂｅｌｉａｎＧｒｏｕｐｓ￥ＭｅｎｇＪｉｘｉａｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉｎｊｉａｎｇＵｎｉｖｅｒｓｉｔｙ，Ｕ... 详细信息

ＩｓｏｍｏｒｐｈｉｓｍｓｏｆＣａｙｌｅｙＤｉｇｒａｐｈｓｏｆＩｎｆｉｎｉｔｅＡｂｅｌｉａｎＧｒｏｕｐｓ￥ＭｅｎｇＪｉｘｉａｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉｎｊｉａｎｇＵｎｉｖｅｒｓｉｔｙ，Ｕｒｕｍｃｈｉ，８３００４６）Ａｂｓ...

关键词： isomerphisms cayley digraphs groups