A family of graphs that are DGS but not DS

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-09-10 DOI:10.1016/j.laa.2025.09.009

Limeng Lin , Luiz Emilio Allem , Vilmar Trevisan , Wei Wang , Hao Zhang

引用次数: 0

Abstract

The spectral characterization of graphs is a central theme in spectral graph theory. A graph G is determined by its spectrum (DS) if every graph cospectral with G is also isomorphic to G. The definition is extended to the generalized spectrum, where a graph G is determined by its generalized spectrum (DGS) if any graph H that is cospectral with G and whose complement is cospectral with

\bar{G}

must be isomorphic to G. While it is clear that all DS graphs are also DGS, the reverse is not always true. This leads to a natural, unanswered question: Which graphs are DGS but not DS? Previous research has focused on identifying graphs that are either DS or DGS, but, to our knowledge, research on this specific problem has not attracted much attention. This paper addresses the problem by introducing an infinite family of graphs that are DGS but not DS.

查看原文本刊更多论文

属于DGS但不是DS的一组图

图的谱表征是谱图理论的一个中心主题。图G是由它的谱（DS）决定的，如果与G共谱的每个图也与G同构，则将定义推广到广义谱，其中图G是由它的广义谱（DGS）决定的，如果任何与G共谱的图H及其补与G共谱的图H必须与G同构，虽然很明显，所有的DS图也是DGS，但反过来并不总是正确的。这就引出了一个自然的、没有答案的问题：哪些图是DGS而不是DS？以前的研究主要集中在识别DS或DGS图形上，但据我们所知，对这一特定问题的研究并没有引起太多关注。本文通过引入一个无限族的图来解决这个问题，这些图是DGS而不是DS。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.