The study of the Laplacian Eignvalues of graphs
碩士令G為一簡單圖且A(G)為圖G的鄰接矩陣,D(G)為圖G的度對角矩陣,其中對角線元素dii為圖G上的點vi的度數,即dii=deg(vi)。定義L(G)=D(G)–A(G)為圖G的拉普拉斯矩陣,此拉普拉斯矩陣的特徵值稱為圖G的拉普拉斯特徵值。已知任一圖的最小拉普拉斯特徵值必為零且其餘皆為正數,而其最大特徵值又稱為此圖的拉普拉斯譜半徑。 設f(n)為拉普拉斯譜半徑恰等於點數n且所有特徵值皆為整數的連通圖之總個數,Fiedler證明了圖G的拉普拉斯特徵值為其點數若且唯若圖G的補圖是不連通的 ...
戴思平; Tai, Su-Ping
core
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