High-ordered spectral characterization of unicyclic graphs

IF 0.5 4区 数学 Q3 MATHEMATICS
Yi-Zheng Fan, Hong Yang, Jian Zheng
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引用次数: 4

Abstract

In this paper we will apply the tensor and its traces to investigate the spectral characterization of unicyclic graphs. Let $G$ be a graph and $G^m$ be the $m$-th power (hypergraph) of $G$. The spectrum of $G$ is referring to its adjacency matrix, and the spectrum of $G^m$ is referring to its adjacency tensor. The graph $G$ is called determined by high-ordered spectra (DHS for short) if, whenever $H$ is a graph such that $H^m$ is cospectral with $G^m$ for all $m$, then $H$ is isomorphic to $G$. In this paper we first give formulas for the traces of the power of unicyclic graphs, and then provide some high-ordered cospectral invariants of unicyclic graphs. We prove that a class of unicyclic graphs with cospectral mates is DHS, and give two examples of infinitely many pairs of cospectral unicyclic graphs but with different high-ordered spectra.
单环图的高阶谱表征
本文将应用张量及其迹来研究单环图的谱表征。设$G$是一个图,$G^m$是$G$的$m$次幂(超图)。$G$的谱是指它的邻接矩阵,$G^m$的谱是指它的邻接张量。图$G$称为由高阶谱决定的图(简称DHS),如果每当$H$是一个图,使得$H^m$与$G^m$对所有$m$都是共谱,则$H$与$G$同构。本文首先给出了单环图幂的迹的公式,然后给出了单环图的一些高阶共谱不变量。证明了一类具有共谱偶的单环图是DHS,并给出了两个具有不同高阶谱的无穷多对共谱单环图的例子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
22
审稿时长
53 weeks
期刊介绍: The Discussiones Mathematicae Graph Theory publishes high-quality refereed original papers. Occasionally, very authoritative expository survey articles and notes of exceptional value can be published. The journal is mainly devoted to the following topics in Graph Theory: colourings, partitions (general colourings), hereditary properties, independence and domination, structures in graphs (sets, paths, cycles, etc.), local properties, products of graphs as well as graph algorithms related to these topics.
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