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chromatic number OF SQUARE OF MAXIMAL OUTERPLANAR GRAPHS

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Applied Mathematics(A Journal of Chinese Universities) 2007年第2期22卷 163-168页

作者： Luo Xiaofang Yiwu Industrial and Commercial College Yiwu 322000 China

Let x（G^2） denote the chromatic number of the square of a maximal outerplanar graph G and Q denote a maximal outerplanar graph obtained by adding three chords y1 y3, y3y5, y5y1 to a 6-cycle y1y2…y6y1. In this paper, it is proved that △ ＋ 1 ≤ x（G^2） ≤△ ＋ 2, and x（G^2） = A ＋ 2 if and only if G is Q, where A represents the maximum degree of G.

关键词： chromatic number maximal outerplanar graph square of graph maximum degree

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CIRCULAR chromatic number AND MYCIELSKI GRAPHS

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Acta Mathematica Scientia 2006年第2期26卷 314-320页

作者：刘红美 College of Science Three Gorges University Yichang 443002China

For a general graph G, M（G） denotes its Mycielski graph. This article gives a number of new sufficient conditions for G to have the circular chromatic number xc（M（G）） equals to the chromatic number x（M（G））, ... 详细信息

关键词： Circular chromatic number Mycielski graphs chromatic number

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The chromatic number of(P_(5),HVN)-free Graphs

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Acta Mathematicae Applicatae Sinica 2024年第4期40卷 1098-1110页

作者： Yian XU School of Mathematics Southeast UniversityNanjing 211189China

Let G be a *** useχ(G)andω(G)to denote the chromatic number and clique number of G respectively.A P_(5)is a path on 5 vertices,and an HVN is a K_(4)together with one more vertex which is adjacent to exactly two vertices of K_(4).Combining with some known result,in this paper we show that if G is(P_(5),HVN)-free,thenχ(G)≤max{min{16,ω(G)+3},ω(G)+1}.This upper bound is almost sharp.

关键词： P_(5) HVN chromatic number clique number

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Geodetic number and Geo-chromatic number of 2-Cartesian Product of Some Graphs

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Open Journal of Discrete Mathematics 2022年第1期12卷 1-16页

作者： Medha Itagi Huilgol B. Divya Department of Mathematics Bengaluru City University Central College Campus Bengaluru India Department of Mathematics Bangalore University Bengaluru India

A set S ⊆ V (G) is called a geodetic set if every vertex of G lies on a shortest u-v path for some u, v ∈ S, the minimum cardinality among all geodetic sets is called geodetic number and is denoted by . A set C ⊆ V (G) is called a chromatic set if C contains all vertices of different colors in G, the minimum cardinality among all chromatic sets is called the chromatic number and is denoted by . A geo-chromatic set Sc ⊆ V (G) is both a geodetic set and a chromatic set. The geo-chromatic number of G is the minimum cardinality among all geo-chromatic sets of G. In this paper, we determine the geodetic number and the geo-chromatic number of 2-cartesian product of some standard graphs like complete graphs, cycles and paths.

关键词： Cartesian Product Grid Graphs Geodetic Set Geodetic number chromatic Set chromatic number Geo-chromatic Set Geo-chromatic number

On the chromatic number of (P₅, C₅, Cricket)-Free Graphs

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Engineering（科研） 2022年第3期14卷 147-154页

作者： Weilun Xu School of Mathematics and Statistics Shandong Normal University Jinan China

For a graph G, let be the chromatic number of G. It is well-known that holds for any graph G with clique number . For a hereditary graph class , whether there exists a function f such that holds for every has been widely studied. Moreover, the form of minimum such an f is also concerned. A result of Schiermeyer shows that every -free graph G with clique number has . Chudnovsky and Sivaraman proved that every -free with clique number graph is -colorable. In this paper, for any -free graph G with clique number , we prove that . The main methods in the proof are set partition and induction.

关键词： P5-Free Graphs chromatic number X-Boundedness

Reexploring the upper bound for the chromatic number of graphs

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Progress in Natural Science:Materials International 2004年第3期 84-86页

作者： LI Shuchao 1,2 * and MAO Jingzhong 1(1. Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China 2. Laboratory of Nonlinear Analysis, Department of Mathematics, Central China Normal University, Wuhan 430079, China)

The upper bound of the chromatic number of simple graphs is explored. Its original idea comes from Coffman, Hakimi and Schmeichel, who recently studied the chromatic number of graphs with strong conditions. In this pa... 详细信息

关键词： chromatic number clique number.

The chromatic number and the Second Largest Eigenvalue of the Laplacian Matrix of a Graph

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The Chromatic Number and the Second Largest Eigenvalue of th...

On Graph Having Clique number α,chromatic number α+1

第六届中国青年运筹与管理学者大会

作者： Liu Xiao-Ping Lin Liang Department of Maths and Physics,Guilin Institute of Technology,Guilin,541004

Let G be a simple graph with n vertices and m edges. In the paper, we present a lower bound for the chromatic number of G as follows:where λ2 is the second largest eigenvalue of the Laplacian matrix of G. Another res... 详细信息

关键词： second largest eigenvalue Laplacian matrix chromatic number bipartite graph

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Journal of Mathematical Research with Applications 1991年第3期 400-400页

作者： Xu Baogang(Dept.Math.Shandong University,Jinan)

Let G is a simple graph,ω(G).△(G)、x(G)are maximum clique number ofG,maximum degree and chromatic number of G ***[2],James defi-nes that(a,b,c)(where a,b,c are positive integer)is graphical if there existsG whichω(G)=a,x(G)=b,△(G)=*** say G is on(a,b,c)and set P(a,b,(a,b,c)=min{|V(G)||G is on(a,b,c)}.All other signs are from[1].

关键词： Graph chromatic number On Graph Having Clique number

Graph Properties and Stratified Presentations of Partially Ordered Sets

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Algebra Colloquium 2016年第1期23卷 51-63页

作者： Jin Guo Tongsuo Wu Department of Mathematics Shanghai Jiaotong University Shanghai 200240 China

In this paper, we introduce some new definitions such as the U＊L＊ condition to describe the zero-divisor graph G = F（P） of a poser P, and give a new and quick proof to a main result in [2, 4]. By deleting a typical vertex with least degree, we provide an algorithm for finding a maximum clique of a finite graph G. We study some properties of the zero-divisor graphs of posets concerning diameters and girths. We also provide stratified presentations of posets.

关键词： poset chromatic number clique number deleting method stratified presentation