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過去のセミナー/2010年度 のバックアップ(No.1)


2010年度 組合せ数学セミナー

  • 世話人: 溝口 佳寛(九大数理),坂内 英一(九大数理),谷口哲至(松江高専)

第1回 2010年 5月 8日(土)

  • 場所: 九州大学 西新プラザ 中会議室(2F)
  • 時間: 12:00-18:00
  • 講演者(予定):
    奥田 隆幸(東大数理),栗原 大武(東北大理),Kissani Perera(九大数理),
    重住 淳一(九大数理),溝口 佳寛(九大数理)。

※ 詳細は決まり次第,お知らせする予定です。

  • Abstract

Kissani Perera [#01-perera]

  • タイトル: Laplacian energy of Directed Graphs
  • アブストラクト:

Energy has been studied in mathematical perspective as well as physical perspective for several years ago. In spectral graph theory, the eigenvalues of several kinds of matrices have been studied, of which Laplacian matrix attracted the greatest attention [2]. Recently, in 2009, Adiga considered Laplacian energy of directed graphs using skew Laplacian matrix, in which degree of vertex is considered as total of the out-degree and the in-degree. Since directed graphs play an important role in identifying the structure of web-graphs as well as communication graphs, we consider Laplacian energy of simple directed graphs, complete directed graphs and their line graphs and find some relations relevant to arc addition of directed graphs by using the general definition of Laplacian(Kirchoff) matrix. Unlike in [1], we derived two types of equations for simple directed graphs and completed directed graphs with vertices. Our objective extended to enumerate the structure of directed graphs using the energy concept. For that we consider the class which consists of non isomorphic graphs with energy less than some and find 47 non isomorphic directed graphs for class .

References
[1] C. Adiga and M. Smitha. On the skew laplacian energy of a digraph. International Mathematics Forum 4, 39:1907—1914, 2009.
[2] D.M. Cvetkovic, M. Doob, and H. Sachs. Normalized cuts and image segmentation. In Spectra of Graphs: Theory and Applications, volume 3, 1995.|