环拼接二部图的零性

IF 0.7 4区 数学 Q2 Mathematics
Sarula Chang, Jianxi Li, Yirong Zheng
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引用次数: 0

摘要

对于一个简单的图 $G$,让 $\eta(G)$ 和 $c(G)$ 的null和圈数 $G$,分别。环拼接二部图是一种连通图,其中每个块都是偶环。Wong et al.(2022)证明,对于每一个环拼接二部图 $G$, $0\leq\eta(G)\leq c(G)+1$。此外,极值图与 $\eta(G) = c(G)+1$ 和 $\eta(G) =0$,分别进行了表征。本文证明了不存在环拼接二部图 $G$ 具有零的任意阶的 $\eta(G)=c(G)$。此外,我们还给出了环拼接二部图的结构表征 $G$ 与零 $\eta(G)=c(G)-1$.
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Nullities of cycle-spliced bipartite graphs
For a simple graph $G$, let $\eta(G)$ and $c(G)$ be the nullity and the cyclomatic number of $G$, respectively. A cycle-spliced bipartite graph is a connected graph in which every block is an even cycle. It was shown by Wong et al. (2022) that for every cycle-spliced bipartite graph $G$, $0\leq\eta(G)\leq c(G)+1$. Moreover, the extremal graphs with $\eta(G) = c(G)+1$ and $\eta(G) =0$, respectively, have been characterized. In this paper, we prove that there is no cycle-spliced bipartite graphs $G$ of any order with nullity $\eta(G)=c(G)$. Furthermore, we also provide a structural characterization on cycle-spliced bipartite graphs $G$ with nullity $\eta(G)=c(G)-1$.
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来源期刊
CiteScore
1.20
自引率
14.30%
发文量
45
审稿时长
6-12 weeks
期刊介绍: The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.
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