期刊論文
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 ) |