On connected graphs of order n with girth g and nullity n-g

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题名:	On connected graphs of order n with girth g and nullity n-g
作者:	Zhou, Q.;Wong, D.;Tam, B.-S.
关键词:	Nullity;Rank;Girth
日期:	2021-12
上传时间:	2023-04-28 16:23:12 (UTC+8)
出版者:	Elsevier Inc.
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.
關聯:	Linear Algebra and Its Applications 630, p.56-68
DOI:	10.1016/j.laa.2021.07.005
显示于类别:	[應用數學與數據科學學系] 期刊論文

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