# 過去のセミナー/2010年度 のバックアップソース(No.1)

* 2010年度 組合せ数学セミナー [#h6f7d21c]
-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) [#p64a8835]
-場所: 九州大学
[[西新プラザ:http://www.kyushu-u.ac.jp/university/institution-use/nishijin/index.htm]] 中会議室(2F)
-時間: 12:00-18:00
-講演者(予定):~

※ 詳細は決まり次第，お知らせする予定です。
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-Abstract
***Kissani Perera [#01-perera] [#fc53ba3e]
-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 &mimetex(n \geq 2); vertices.
Our objective extended to enumerate the structure
of directed graphs using the energy concept.
For that we consider the class &mimetex(P(\alpha));
which consists of non isomorphic graphs with energy less than some &mimetex(\alpha);
and find 47 non isomorphic directed graphs for class &mimetex(P(10));.

''References''~
[1] C. Adiga and M. Smitha. On the skew laplacian energy of a digraph. '''International Mathematics Forum''' 4, 39:1907&#x2014;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.|
//|:-:|重住淳一|On maximality of distance sets with the structure of Johnson scheme|
//||>|In the classification of the maximal 2-distance sets, Lison&#277;k considered the 2-distance sets which include the structure of triangular graph '''T'''('''n''') (= '''J'''('''n''', 2)). As a generalization, we consider the maximal distance sets on &mimetex(\mathbb{R}^{n-1}); with the structure of Johnson scheme '''J'''('''n''', '''m'''). In this talk, we determine the condition that the realizations of '''J'''('''n''', '''m''') on &mimetex(\mathbb{R}^{n-1}); should be maximal. Furthermore, we would like to talk about some maximal distance sets with the structure of Johnson scheme. &br; This is joint work with Eiichi Bannai and some members of the program &ldquo;Excellent Students in Science&rdquo; of Fuculty of Science, Kyushu University.|

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