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A DEGREE SEQUENCE METHOD FOR THE CUTWIDTH PROBLEM OF graphS

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Applied Mathematics(A Journal of Chinese Universities) 2002年第2期17卷 125-134页

作者： Lin Yixun Li Xianglu Yang Aifeng Dept. of Math. Zhengzhou Univ. Henan China

The cutwidth problem fora graph G is to embed G into a path such thatthe maximum number of overlap edges is *** paperpresents an approach based on the degree se- quence of G for determining the exact value of cutwidth of typical graphs (e.g.,n- cube,cater- pillars) .Relations between the cutwidth and other graph- theoretic parameters are studied as wel

关键词： combinatorial optimization graph labeling cutwidth bandwidth

CYCLIC BANDWIDTH SUM OF graphS

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Applied Mathematics(A Journal of Chinese Universities) 2001年第2期16卷 115-121页

作者： Hao JianxiuDept.ofMath.,ZhengzhouUniv.,Zhengzhou450052,Dept.ofMath.,AnyangTeachersCollege,Anyang45500 郑州大学河南郑州 450052

Let G be a simple graph. The cyclic bandwidth sum problem is to determine a labeling of graph G in a cycle such that the total length of edges is as small as possible. In this paper, some upper and lower bound... 详细信息

关键词： graph labeling cyclic bandwidth sum optimal cyclic labeling.

THE CUTWIDTH OF TREES WITH DIAMETER AT MOST 4

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Applied Mathematics(A Journal of Chinese Universities) 2003年第3期18卷 361-369页

作者： Lin YixunDept.of Math., Zhengzhou Univ., Zhengzhou 450052, China. Dept. of Math. Zhengzhou Univ. Zhengzhou China

The cutwidth problem for a graph G is to embed G into a path P n such that the maximum number of overlap edges (i.e., the congestion) is minimized. It is known that the problem for general graphs is NP-hard while it is polynomially solvable for trees. This paper presents an exact formula for the cutwidth of trees with diameter at most 4. A relation with the bandwidth is discussed as well.

关键词： graph labeling cutwidth bandwidth trees with diameter 4

Edge Product Cordial labeling of Some Cycle Related graphs

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Open Journal of Discrete Mathematics 2016年第4期6卷 268-278页

作者： Udayan M. Prajapati Nittal B. Patel St. Xavier’s College Ahmedabad India Shankersinh Vaghela Bapu Institute of Technology Gandhinagar India

For a graph having no isolated vertex, a function is called an edge product cordial labeling of graph G, if the induced vertex labeling function defined by the product of labels of incident edges to each vertex is such that the number of edges with label 0 and the number of edges with label 1 differ by at most 1 and the number of vertices with label 0 and the number of vertices with label 1 also differ by at most 1. In this paper, we discuss edge product cordial labeling for some cycle related graphs.

关键词： graph labeling Edge Product Cordial labeling

Some Edge Product Cordial graphs in the Context of Duplication of Some graph Elements

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Open Journal of Discrete Mathematics 2016年第4期6卷 248-258页

作者： Udayan M. Prajapati Prakruti D. Shah St. Xavier’s College Ahmedabad India Shankersinh Vaghela Bapu Institute of Technology Gandhinagar India

For a graph, a function is called an edge product cordial labeling of G, if the induced vertex labeling function is defined by the product of the labels of the incident edges as such that the number of edges with label 1 and the number of edges with label 0 differ by at most 1 and the number of vertices with label 1 and the number of vertices with label 0 differ by at most 1. In this paper, we show that the graphs obtained by duplication of a vertex, duplication of a vertex by an edge or duplication of an edge by a vertex in a crown graph are edge product cordial. Moreover, we show that the graph obtained by duplication of each of the vertices of degree three by an edge in a gear graph is edge product cordial. We also show that the graph obtained by duplication of each of the pendent vertices by a new vertex in a helm graph is edge product cordial.

关键词： graph labeling Edge Product Cordial labeling Duplication of a Vertex

MAXIMUM CUTWIDTH PROBLEM FOR graphS

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Applied Mathematics(A Journal of Chinese Universities) 2003年第2期18卷 235-242页

作者： Hao JianxiuDept. of Math.,Zhejiang Normal Univ.,Jinhua 321004,China. Dept. of Math. Zhejiang Normal Univ. Jinhua China

The problem studied in this paper is to determine E(p,C),the maximum size of a connected graph G with the given vertex number p and cutwidth C. This paper presents some results on this problem.

关键词： graph labeling cutwidth extremal graph.

Extremal Cut-width Problem for graphs

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Chinese Quarterly Journal of Mathematics 2006年第1期21卷 38-43页

作者： HAO Jian-xiu YANG Ai-feng Department of Mathematics Zhejiang Normal University Jinhua 321004 China School of Mathematical Sciences South China University of Technology Guangzhou 510641 China

The problem studied in this paper is to determine e（p, C）, the minimum size of a connected graph G with given vertex number p and cut-width C.

关键词： graph labeling cut-width extremal graph

The Interval graph Completion Problem on Split graphs

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Chinese Quarterly Journal of Mathematics 2015年第2期30卷 308-316页

作者： ZHANG Zhen-kun YU Min Department of Mathematics Huanghuai University Zhumadian 463000 China Software College Zhengzhou Raiway Vocational and Technical College Zhengzhou 450052 China

The interval graph completion problem on a graph G is to find an added edge set F such that G + F is an interval supergraph with the smallest possible number of edges. The problem has important applications to numerical algebra, V LSI-layout and algorithm graph theory etc; And it has been known to be N P-complete on general graphs. Some classes of special graphs have been investigated in the literatures. In this paper the interval graph completion problem on split graphs is investigated.

关键词： interval graph graph labeling graph completion split graph

Forming a Critical Tree with Cutwidth k

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Chinese Quarterly Journal of Mathematics 2022年第4期37卷 366-379页

作者： ZHANG Zhen-kun YE Xi-qiong School of Mathematics and Statistics Huanghuai UniversityZhumadian 463000China Zhengzhou Electronic Information Engineering College Zhenzhou 450007China

The cutwidth of a graph G is the minimum number of overlap edges when G is embedded into a path *** cutwidth problem for a graph G is to determine the cutwidth of G.A graph G with cutwidth k is k-cutwidth critical if every proper subgraph of G has cutwidth less than k and G is homeomorphically *** this paper,we completely investigated methods of forming a k-cutwidth(k>1)critical tree T.

关键词： Combinatorics graph labeling Cutwidth Critical tree