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The (⊿+2,2)-incidence coloring of outerplanar graphs

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Progress in Natural Science:Materials International 2008年第5期18卷 575-578页

作者： Shudong Wanga,b,c, Jin Xu a,b, Fangfang Mac, Chunxiang Xua,b a Institute of Software, School of Electronic Engineering and Computer Science, Peking University, Beijing 100871, China b Key Laboratory of High Con dence Software Technologies, Ministry of Education, Beijing 100871, China c College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, China Institute of Software School of Electronic Engineering and Computer Science Peking University Beijing 100871 China Key Laboratory of High Confidence Software Technologies Ministry of Education Beijing 100871 China College of Information Science and Engineering Shandong University of Science and Technology Qingdao 266510 China

An incidence coloring of graph G is a coloring of its incidences in which neighborly incidences are assigned di erent colors. In this paper, the incidence coloring of outerplanar graphs is discussed using the techniques of exchanging colors and the double inductions from the aspect of con guration property. Results show that there exists a (D + 2,2)-incidence coloring in every outerplanar graph, where D is the maximum degree of outerplanar graph.

关键词： incidence coloring incidence chromatic number Outerplanar graph

Conflict-free incidence coloring of Outer-1-planar Graphs

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Acta Mathematicae Applicatae Sinica 2024年第4期40卷 929-942页

作者： Meng-ke QI Xin ZHANG School of Mathematics and Statistics Xidian UniversityXi’an 710071China

An incidence of a graph G is a vertex-edge pair(v,e)such that v is incidence with e.A conflict-free incidence coloring of a graph is a coloring of the incidences in such a way that two incidences(u,e)and(v,f)get distinct colors if and only if they conflict each other,i.e.,(i)u=v,(ii)uv is e or f,or(iii)there is a vertex w such that uw=e and vw=*** minimum number of colors used among all conflict-free incidence colorings of a graph is the conflict-free incidence chromatic number.A graph is outer-1-planar if it can be drawn in the plane so that vertices are on the outer-boundary and each edge is crossed at most *** this paper,we show that the conflict-free incidence chromatic number of an outer-1-planar graph with maximum degree△is either 2△or 2△+1 unless the graph is a cycle on three vertices,and moreover,all outer-1-planar graphs with conflict-free incidence chromatic number 2△or 2△+1 are completely *** efficient algorithm for constructing an optimal conflict-free incidence coloring of a connected outer-1-planar graph is given.

关键词： outer-1-planar graph incidence coloring combinatorial algorithm channel assignment problem

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Adjacent Vertex Distinguishing incidence coloring of the Cartesian Product of Some Graphs

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Journal of Mathematical Research and Exposition 2011年第2期31卷 366-370页

作者： Qian WANG Shuang Liang TIAN Department of Mathematics and Computer Science Northwest University for Nationalities Gansu 730030 P. R. China

An adjacent vertex distinguishing incidence coloring of graph G is an incidence coloring of G such that no pair of adjacent vertices meets the same set of *** obtain the adjacent vertex distinguishing incidence chroma... 详细信息

关键词： Cartesian product incidence coloring adjacent vertex distinguishing incidence coloring adjacent vertex distinguishing incidence chromatic number

The incidence coloring Number of Complete k-Partite Graph

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Journal of China University of Mining and Technology 2001年第1期11卷 87-89页

作者：刘西奎李艳 DepartmentofControlScience＆Engineering HuazhongUniversityofScienceandTechnologyWuhanHubei430074P.R.China DepartmentofBasicScienceofTechnology EducationofXuzhouNormalUniversityXuzhouJiangsu221011P.R.China

The concept of the incidence chromatic number of a graph was introduced by Brualdi and Massey. They conjectured that every graph G can be incidence colored with Δ (G) +2 colors. In this paper, the trueness of this conjecture for complete k partite graph was proved, and the incidence chromatic number of complete k partite graphs was calculated.

关键词： incidence set incidence coloring incidence chromatic number

incidence colorings of Powers of Circuits

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Chinese Quarterly Journal of Mathematics 2010年第2期25卷 159-167页

作者： LI De-ming LIU Ming-ju Department of Mathematics Capital Normal University Beijing 100037 China LMIB and Department of Mathematics Beihang University Beijing 100083 China

The incidence chromatic number of G is the least number of colors such that G has an incidence coloring. It is proved that the incidence chromatic number of Cn^p, the p-th power of the circuit graph, is 2p ＋ 1 if and only if n = k（2p ＋ 1）, for other cases： its incidence chromatic number is at most 2p ＋ [r/k] ＋ 2, where n = k（p ＋ 1）＋ r, k is a positive integer. This upper bound is tight for some cases.

关键词： incidence coloring circuit powers partition