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On the relation between the adjacency rank of a complex unit gain graph and the matching number of its underlying graph
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2020-06-11 , DOI: 10.1080/03081087.2020.1776205 Shuchao Li 1 , Ting Yang 1
中文翻译:
复单位增益图的邻接秩与其底层图匹配数的关系
更新日期:2020-06-11
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2020-06-11 , DOI: 10.1080/03081087.2020.1776205 Shuchao Li 1 , Ting Yang 1
Affiliation
ABSTRACT
Let be an n-vertex complex unit gain graph and let G be its underlying graph. The adjacency rank of , written as , is the rank of its adjacency matrix and denote by the matching number of the underlying graph G. In this contribution, based on combinatorial interpretation of all the coefficients of the characteristic polynomial of , we determine sharp upper and lower bounds on Furthermore, we establish sharp lower bounds on and . All the corresponding extremal complex unit gain graphs are characterized.
中文翻译:
复单位增益图的邻接秩与其底层图匹配数的关系
摘要
让是一个n顶点复单位增益图,并让G是它的基础图。邻接等级,写为, 是其邻接矩阵的秩,表示为底层图G的匹配数。在这个贡献中,基于对特征多项式的所有系数的组合解释,我们确定尖锐的上限和下限此外,我们在和. 所有相应的极值复单位增益图都被表征。