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3-调和的5-圈图 被引量:1

Three-harmonic Pentacyclic Graph
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摘要 设v1,v2,v3,…,vn是图G的n个顶点,若(d(v1),d(v2),d(v3),…,d(vn))T是图G邻接矩阵A的特征向量,则称G是调和图,其中d(vi)表示顶点vi的度.1-4圈的调和图已经确定,本文确定了所有的3-调和的5-圈调和图. A graph G on nvertice v1,v2,…,v, is said to be harmonic if (d(v1),d(v2),d(v3),…,d(vn))^T is an eigenvector of its adjacency matrix A,where d(vi) is the degree of the vertex vi,i= 1,2,3…,n. Earlier all unicyclic, bicyclic,tricyclic and tetracyclic harmonic graphs were determined. In this paper,we determined all three-harmonic pentracyclic graphs,
作者 曹磊
出处 《数学理论与应用》 2005年第3期56-59,共4页 Mathematical Theory and Applications
基金 湖南省教育厅科学研究资助项目(03B019)
关键词 调和图 特征值 连通图 5-圈图 圈图 特征向量 矩阵A 顶点 图G 邻接 Harmonic graphs Eigenvalues Connected graphs Pentracyclic graphs.
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参考文献4

  • 1S. Grunewald,Harmonic tree,Appl. Math. Letters . 2002
  • 2B. Borovicanin,S. Grunewald,I . Gutman,M. Petrovic.Harmonic graphs with small number of cycles[].Discrete Mathematics.2003
  • 3A. Dress and I . Gutman.On the number of walks in a graph, Appl[].Math Letters.2003
  • 4A. Dress and I . Gutman.Asymptotic results regarding the number of walks in a graph, Appl[].Math Letters.2003

同被引文献5

  • 1CVETKOVIC D M,ROWLINSON P,SIMI(C) S.Eigenspaces of graphs[M].Cambridge:Cambridge Univ Press,1997.
  • 2DRESS A,GUTMAN I.On the number of walks in a graph[J].Appl Math Letters,2003,16:797-801.
  • 3GR(U)NEWALD S.Harmonic tree[J].Appl Math Letters,2002,15(8):1 001-1 004.
  • 4BOROVICANIN B,GR(U)NEWALD S,GUTMAN I,et al.Tetracyclic harmonic graphs[J].BULLETIN T.CXXIII del' Académic Serbe des Art-2002 Classe des Sciences mathématiqueset naturelles Sciences mathématiques,2002,27:19-31.
  • 5BOROVI(C)ANIN B,GR(U)NEWALD S,GUTMAN I.Harmonic graphs with small number of cycles[J].Discrete Math,2003,265:31-34.

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