Graphs whose adjacency matrices have rank equal to the number of distinct nonzero rows

doi:10.1016/j.laa.2012.06.027

淡江大學機構典藏 > 理學院 > 數學學系暨研究所 > 期刊論文 > Item 987654321/89144

請使用永久網址來引用或連結此文件: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/89144

題名:	Graphs whose adjacency matrices have rank equal to the number of distinct nonzero rows
作者:	Huang, Liang-Hao;Tam, Bit-Shun;Wu, Shu-Hui
貢獻者:	淡江大學數學學系
關鍵詞:	Rank;Adjacency matrix;Reduced adjacency matrix;Reduced graph;Number of distinct nonzero rows;Cograph;Neighborhood equivalence classes
日期:	2013-05-15
上傳時間:	2013-05-22 10:41:06 (UTC+8)
出版者:	Philadelphia: Elsevier Inc.
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.
關聯:	Linear Algebra and its Applications 438(10), pp.4008-4040
DOI:	10.1016/j.laa.2012.06.027
顯示於類別:	[數學學系暨研究所] 期刊論文

文件中的檔案:

檔案	大小	格式	瀏覽次數
Graphs whose adjacency matrices have rank equal to the number of distinct nonzero rows.pdf	512Kb	Adobe PDF	1	檢視/開啟
index.html	0Kb	HTML	310	檢視/開啟
index.html	0Kb	HTML	65	檢視/開啟

在機構典藏中所有的資料項目都受到原著作權保護.

TAIR相關文章

資料載入中.....