演講公告

新聞標題：　( 2010-11-25 )

• 演講主題：Some recent results in algebraic graph theory

• 主講人：葉鴻國 教授 (中央大學數學系)

• 演講日期：2010年11月30日(星期二) 下午2:00 –3:00

• 演講地點：(光復校區)科學一館223室

• 茶會時間：當天下午1:30

• 摘要內容：
  

  The rank of a graph G is de¯ned to be the rank (over R) of its adjacency matrix.
  In the ¯rst part of the talk, we consider the following problem: What is the structure
  of a connected graph with rank 4? In this talk, we resolve this question by completely
  characterizing graphs G whose adjacency matrix has rank 4. Given a graph G on n
  vertices and a ¯eld F, the maximum nullity of G over F, denoted by MF (G), is the
  largest possible nullity over all n £ n symmetric matrices over F whose (i; j)th entry
  (for i 6= j) is nonzero whenever ij is an edge in G and is zero otherwise. The maximum
  nullity problem of a graph G is to determine MF (G). In 2008, the AIM Minimum
  Rank{Special Graphs Work Group introduced a new graph parameter Z(G), the zero
  forcing number, to bound MF (G) from above. The authors posted the following ques-
  tion: What is the class of graphs G for which Z(G) = MF (G) for some ¯eld F? In
  the second part of this talk, selected recent results on the question will be presented.
  If time permits, I'll also sketch our work done on the rank of a cograph. This talk is
  based on joint papers with Prof. Gerard J. Chang (National Taiwan University) and
  Dr. Liang-Hao Huang (National Central University).

• 相關檔案：演講991130.doc




• 相關檔案：11_30.pdf

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