教師資料查詢 | 類別: 期刊論文 | 教師: 譚必信 Tam Bit-shun (瀏覽個人網頁)

標題:Graphs whose adjacency matrices have rank equal to the number of distinct nonzero rows
學年101
學期2
出版(發表)日期2013/05/15
作品名稱Graphs whose adjacency matrices have rank equal to the number of distinct nonzero rows
作品名稱(其他語言)
著者Huang, Liang-Hao; Tam, Bit-Shun; Wu, Shu-Hui
單位淡江大學數學學系
出版者Philadelphia: Elsevier Inc.
著錄名稱、卷期、頁數Linear Algebra and its Applications 438(10), pp.4008-4040
摘要For a simple graph G, let rank(G) and dnzr(G) denote respectively the rank and the number of distinct nonzero rows of the adjacency matrix A(G) of G. Equivalent conditions are given for the join G1∨G2 of two vertex-disjoint graphs G1,G2 to satisfy rank(G1∨G2)=dnzr(G1∨G2). A new proof is provided for the known relation rank(G) = dnzr(G) for cographs G. Our approach relies on the concepts of neighborhood equivalence classes, reduced graph and reduced adjacency matrix, and also on a known result that relates the spectrum of the adjacency matrix of a graph with that of its reduced adjacency matrix as well as a new characterization of the nonsingularity of a real symmetric matrix in a special 2 × 2 block form. Our treatment provides ways to construct graphs G, other than cographs, that satisfy rank(G) = dnzr(G). As a side result we also show that every rational number is equal to the sum of the entries of the inverse of the adjacency matrix of a connected nonsingular graph.
關鍵字Rank;Adjacency matrix;Reduced adjacency matrix;Reduced graph;Number of distinct nonzero rows;Cograph;Neighborhood equivalence classes
語言英文(美國)
ISSN0024-3795
期刊性質國外
收錄於SCI;
產學合作
通訊作者Tam, Bit-Shun
審稿制度
國別美國
公開徵稿
出版型式,電子版,紙本
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