Characterization of strongly regular integral circulant graphs by spectral approach

IF 1 4区数学 Q1 MATHEMATICS

Applicable Analysis and Discrete Mathematics Pub Date : 2022-01-01 DOI:10.2298/aadm180713023b

Milan Basic

引用次数: 3

Abstract

The integral circulant graph ICGn(D) has the vertex set Zn = {0, 1, 2, . . . , n? 1} and vertices a and b are adjacent if gcd(a ? b, n) ? D, where D ? Dn, Dn = {d : d | n, 1 ? d < n}. Motivated by the incorrect proof of a previously published result, in this paper we characterize the class of integral circulant graphs that are strongly regular. More precisely, connected ICGn(D) is strongly regular if and only if n is composite and D = {d ? Dn | m ? d} for some m | n and n ? 1 ? m ? 2.

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用谱法刻画强正则积分循环图

积分循环图ICGn(D)的顶点集Zn ={0,1,2，…n ?如果gcd(a ?B, n) ?D，哪里D ?Dn, Dn = {d: d | n, 1 ?D < n}。基于先前发表的一个结果的错误证明，本文刻画了一类强正则的积分循环图。更准确地说，连通ICGn(D)是强正则的当且仅当n是复合且D = {D ?不是bbbbm吗?D}对于某个m b| n和n ?1 ？ m ?2.

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

Applicable Analysis and Discrete Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Applicable Analysis and Discrete Mathematics is indexed, abstracted and cover-to cover reviewed in: Web of Science, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), Mathematical Reviews/MathSciNet, Zentralblatt für Mathematik, Referativny Zhurnal-VINITI. It is included Citation Index-Expanded (SCIE), ISI Alerting Service and in Digital Mathematical Registry of American Mathematical Society (http://www.ams.org/dmr/).