This website requires JavaScript.

On the nullities of quartic circulant graphs and their extremal null spaces

Ivan Damnjanovi\'c
Dec 2022
摘要
A circulant graph is a simple graph whose adjacency matrix can be representedin the form of a circulant matrix, while a nut graph is considered to be agraph whose null space is spanned by a single full vector. In a previous studyby Damnjanovi\'c [arXiv:2212.03026, 2022], the complete set of all the pairs$(n, d)$ for which there exists a $d$-regular circulant nut graph of order $n$has been determined. Motivated by the said results, we put our focus on thequartic circulant graphs and derive an explicit formula for computing theirnullities. Furthermore, we implement the aforementioned formula in order toobtain a method for inspecting the singularity of a particular quarticcirculant graph and find the concise criteria to be used for testing whethersuch a graph is a nut graph. Subsequently, we compute the minimum and maximumnullity that a quartic circulant graph of a fixed order $n$ can attain, foreach viable order $n \ge 5$. Finally, we determine all the graphs attainingthese nullities and then provide a full characterization of all of theircorresponding extremal null spaces.
展开全部
图表提取

暂无人提供速读十问回答

论文十问由沈向洋博士提出,鼓励大家带着这十个问题去阅读论文,用有用的信息构建认知模型。写出自己的十问回答,还有机会在当前页面展示哦。

Q1论文试图解决什么问题?
Q2这是否是一个新的问题?
Q3这篇文章要验证一个什么科学假设?
0
被引用
笔记
问答