| Graphs with maximal signless Laplacian spectral radius | |
|---|---|
| 學年 | 98 |
| 學期 | 2 |
| 出版（發表）日期 | 2010-03-01 |
| 作品名稱 | Graphs with maximal signless Laplacian spectral radius |
| 作品名稱（其他語言） | |
| 著者 | Chang, Ting-Jung; Tam, Bit-Shun |
| 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.1708–1733 |
| 摘要 | By the signless Laplacian of a (simple) graphG we mean the matrix Q(G) = D(G)+A(G), where A(G), D(G) denote respectively the adjacency matrix and the diagonal matrix of vertex degrees ofG. It is known that connected graphs G that maximize the signless Laplacian spectral radius ρ(Q(G)) over all connected graphs with given numbers of vertices and edges are (degree) maximal. For a maximal graph G with n vertices and r distinct vertex degrees δr > δr−1 >··· > δ1, it is proved that ρ(Q(G)) < ρ(Q(H))for some maximal graph H with n+1 (respectively, n) vertices and the same number of edges as G if either G has precisely two dominating vertices or there exists an integer i,2 ≦ i ≦ [r/2] (respectively, if there exist positive integers i, lwithl + 2 ≦ i ≦ [r/2] such that δi + δr+1−i ≦ n+1 (respectively, δi + δr+1−i ≦ δl + δr−l + 1). Graphs that maximize ρ(Q(G)) over the class of graphs with m edges and m−k vertices, for k = 0,1,2,3, are completely determined. |
| 關鍵字 | Signless Laplacian; Maximal graphs; Spectral radius; Line graph |
| 語言 | en |
| ISSN | 0024-3795 |
| 期刊性質 | 國外 |
| 收錄於 | SCI EI |
| 產學合作 | |
| 通訊作者 | Tam, Bit-shun Tam, Bit-Shun |
| 審稿制度 | 是 |
| 國別 | USA |
| 公開徵稿 | |
| 出版型式 | 紙本 |
| 相關連結 |
機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/58742 ) |
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