| 符号圈拼接图的零度 |
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| 引用本文： | 常萨如拉,李建喜,郑艺荣. 符号圈拼接图的零度[J]. 数学研究及应用, 2023, 43(6): 631-647 |
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| 作者姓名： | 常萨如拉 李建喜 郑艺荣 |
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| 作者单位： | 内蒙古农业大学理学院, 内蒙古 呼和浩特 010000;闽南师范大学数学与统计学院, 福建 漳州 363000;厦门理工学院数学与统计学院, 福建 厦门 361000 |
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| 基金项目： | 内蒙古自然科学基金(Grant No.2020BS01011), 国家自然科学基金(Grant No.12171089), 福建省自然科学基金(Grant No.2021J02048), 厦门理工学院科研项目(Grant Nos.YKJ20018R; XPDKT20039). |
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| 摘 要： | 令$eta(Gamma)$和$c(Gamma)$是符号图$Gamma$的零度和基本圈数. 一个符号圈拼接图是指每个块都是圈的连通符号图. 本文证明了对任意符号拼接图$eta(Gamma)le c(Gamma)+1$成立, 并且刻画了等号成立的极图, 推广了王登银等人(2022)在简单圈拼接图上的结果. 此外, 我们证明了任意的符号拼接图$eta(Gamma)neq c(Gamma)$, 给出了满足$eta(Gamma)=c(Gamma)-1$的符号拼接图的一些性质并刻画处$eta(Gamma)=c(Gamma)-1$的二部符号拼接图.
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| 关 键 词： | 符号图 零度 基本圈数 |
| 收稿时间： | 2022-12-14 |
| 修稿时间： | 2023-04-25 |
The Nullities of Signed Cycle-Spliced Graphs |
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| Sarula CHANG,Jianxi LI,Yirong ZHENG. The Nullities of Signed Cycle-Spliced Graphs[J]. Journal of Mathematical Research with Applications, 2023, 43(6): 631-647 |
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| Authors: | Sarula CHANG Jianxi LI Yirong ZHENG |
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| Affiliation: | College of Science, Inner Mongolia Agricultural University, Inner Mongolia 010018, P. R. China;School of Mathematics and Statistics, Minnan Normal University, Fujian 363000, P. R. China; School of Mathematics and Statistics, Xiamen University of Technology, Fujian 361000, P. R. China |
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| Abstract: | Let $eta(Gamma)$ and $c(Gamma)$ be the nullity and the cyclomatic number of a signed graph $Gamma$. A signed cycle-spliced graph is a connected signed graph in which every block is a cycle. In this paper, we prove that for every signed cycle-spliced graph $Gamma$, $eta(Gamma)leq c(Gamma)+1$ and the extremal graphs $Gamma$ with nullity $c(Gamma)+1$ are characterized, which extend the related results of Wong, Zhou and Tian (2022) on simple cycle-spliced graphs. Moreover, we prove that for every signed cycle-spliced graph $Gamma$, $eta(Gamma)neq c(Gamma)$. Some properties on signed cycle-spliced graphs $Gamma$ with $eta(Gamma)= c(Gamma)-1$ are explored, as well as a structural characterization on signed cycle-spliced bipartite graphs $Gamma$ satisfying $eta(Gamma)= c(Gamma)-1$. |
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| Keywords: | signed graph nullity cyclomatic number |
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