| On connected graphs of order n with girth g and nullity n-g | |
|---|---|
| 學年 | 110 |
| 學期 | 1 |
| 出版（發表）日期 | 2021-12-01 |
| 作品名稱 | On connected graphs of order n with girth g and nullity n-g |
| 作品名稱（其他語言） | |
| 著者 | Q. Zhou; D. Wong; B.-S. Tam |
| 單位 | |
| 出版者 | |
| 著錄名稱、卷期、頁數 | Linear Algebra and Its Applications 630, p.56-68 |
| 摘要 | Let G be a simple graph of order n. The nullity of a graph G, denoted by , is the multiplicity of 0 as an eigenvalue of its adjacency matrix. If G has at least one cycle, then the girth of G, denoted by , is the length of the shortest cycle in G. It is known that is bounded above by if and by if . In this paper it is proved that when G is connected, if and only if G is a complete bipartite graph, different from a star, or a cycle of length a multiple of 4; that if G is not a complete bipartite graph or a cycle of length a multiple of 4, then . Connected graphs of order n with girth g and nullity are characterized. This work also settles the problem of characterizing connected graphs with rank equal to girth and the problem of identifying all connected graphs G that contains a given nonsingular cycle as a shortest cycle and with the same rank as G. |
| 關鍵字 | Nullity;Rank;Girth |
| 語言 | en_US |
| ISSN | 0024-3795;1873-1856 |
| 期刊性質 | 國外 |
| 收錄於 | SCI |
| 產學合作 | |
| 通訊作者 | |
| 審稿制度 | 否 |
| 國別 | USA |
| 公開徵稿 | |
| 出版型式 | ,電子版,紙本 |
| 相關連結 |
機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/122892 ) |
GoogleAnalytics