朱佳敏,李双东.关于混合图H-秩的一个注记[J].安徽建筑大学学报,2021,29(): |
关于混合图H-秩的一个注记 |
A note on H-rank of mixed graph |
投稿时间:2021-01-05 修订日期:2021-01-25 |
DOI:10.11921/j.issn.2095-8382.20210105002 |
中文关键词: 混合图 H-秩 匹配数 圈空间维数 |
英文关键词: Mixed graph H-rank Matching number Cyclomatic number |
基金项目:国家自然科学基金项目(面上项目) |
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中文摘要: |
关于以图G为底图的混合图G'的H-秩,李书超等人[Linear and Multilinear Algebra, 2018, 66 (9): 1853-1869]证明了rk(G')的下界为2m(G)-2c(G),上界为2m(G)+c(G)。本文证明了不存在rk(G')=2m(G)-2c(G)+1的混合图,并且存在无穷多个连通混合图G',满足c(G)=k,rk(G)=2m(G)-2c(G)+l,其中k为非负整数,l为不大于3k的非1正整数。 |
英文摘要: |
For any mixed graph G' , Chen, Huang and Li [Linear and Multilinear Algebra, 2018, 66 (9): 1853-1869] proved that rk(G') has the lower bound 2m(G)-2c(G), the upper bound 2m(G)+c(G) . In this paper, we prove that there is no mixed graph G' with rk(G')=2m(G)-2c(G)+1 , and in addition, there are infinitely many connected mixed graphs G' such that c(G)=k and rk(G')=2m(G)-2c(G)+l for every integers k,l , satisfying 0 |
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