分割符号图的谱分析

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Sandeep Kumar, Deepa Sinha
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引用次数: 0

摘要

有序对 $\Sigma = (\Sigma^{u}$,$\sigma$)称为有符号图,其中 $\Sigma^{u} = (V,E)$ 是一个有符号图,$\sigma$是从 $E$ 到符号集 $\lbrace +, - \rbrace$ 的有符号映射,称为有符号图。有符号图 $\Sigma$ 的文本{拆分有符号图} $\Gamma(\Sigma)$ 定义为:对于 V(\Sigma)$ 中的每个顶点 $u,取一个新顶点 $u'$。将 $u'$ 连接到 $\Sigma$ 中所有与 $u$ 相邻的顶点,使得 $\sigma_{\Gamma}(u'v) = \sigma(u'v), \ u \in N(v)$.本文的目的是提出一种算法,利用 Matlab 从给定的带符号图生成分裂带符号图和分裂根带符号图。此外,我们还对生成的图进行了频谱分析。对分裂签名图的邻接矩阵和拉普拉斯矩阵进行频谱分析,以研究其特征值和特征向量。建立了原始有符号图的能量 $\Sigma$ 和分裂有符号图的能量 $\Gamma(\Sigma)$ 之间的关系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Spectral Analysis of Splitting Signed Graph
An ordered pair $\Sigma = (\Sigma^{u}$,$\sigma$) is called the \textit{signed graph}, where $\Sigma^{u} = (V,E)$ is a \textit{underlying graph} and $\sigma$ is a signed mapping, called \textit{signature}, from $E$ to the sign set $\lbrace +, - \rbrace$. The \textit{splitting signed graph} $\Gamma(\Sigma)$ of a signed graph $\Sigma$ is defined as, for every vertex $u \in V(\Sigma)$, take a new vertex $u'$. Join $u'$ to all the vertices of $\Sigma$ adjacent to $u$ such that $\sigma_{\Gamma}(u'v) = \sigma(u'v), \ u \in N(v)$. The objective of this paper is to propose an algorithm for the generation of a splitting signed graph, a splitting root signed graph from a given signed graph using Matlab. Additionally, we conduct a spectral analysis of the resulting graph. Spectral analysis is performed on the adjacency and laplacian matrices of the splitting signed graph to study its eigenvalues and eigenvectors. A relationship between the energy of the original signed graph $\Sigma$ and the energy of the splitting signed graph $\Gamma(\Sigma)$ is established.
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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