On the reduced signless Laplacian spectrum of a degree maximal graph
學年 98
學期 2
出版（發表）日期 2010-03-15
作品名稱 On the reduced signless Laplacian spectrum of a degree maximal graph
作品名稱（其他語言）
著者 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 432(7), pp.1734-1756
摘要 For a (simple) graph G, the signless Laplacian of G is the matrix A(G)+D(G), where A(G) is the adjacency matrix and D(G) is the diagonal matrix of vertex degrees of G; the reduced signless Laplacian of G is the matrix Δ(G)+B(G), where B(G) is the reduced adjacency matrix of G and Δ(G) is the diagonal matrix whose diagonal entries are the common degrees for vertices belonging to the same neighborhood equivalence class of G. A graph is said to be (degree) maximal if it is connected and its degree sequence is not majorized by the degree sequence of any other connected graph. For a maximal graph, we obtain a formula for the characteristic polynomial of its reduced signless Laplacian and use the formula to derive a localization result for its reduced signless Laplacian eigenvalues, and to compare the signless Laplacian spectral radii of two well-known maximal graphs. We also obtain a necessary condition for a maximal graph to have maximal signless Laplacian spectral radius among all connected graphs with given numbers of vertices and edges.
關鍵字 Degree maximal graph; Reduced signless Laplacian; Signless Laplacian spectrum; Characteristic polynomial; Neighborhood equivalence class
語言 en
ISSN 0024-3795
期刊性質 國外
收錄於 EI SCI
產學合作
通訊作者 Tam, Bit-Shun
審稿制度
國別 USA
公開徵稿
出版型式
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