{"title":"Alternating L-functions of finite digraphs","authors":"Yongjiang Wu, Lihua Feng, Weijun Liu","doi":"10.1016/j.dam.2025.03.009","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we provide a new proof for the Ihara expression of the alternating <span><math><mi>L</mi></math></span>-function of a digraph. Furthermore, we present a relation between the weighted alternating <span><math><mi>L</mi></math></span>-function of a digraph and that of the quotient of its regular covering. As an application, we give a decomposition formula for the weighted alternating zeta function of the quotient of a regular covering of a digraph by its weighted alternating <span><math><mi>L</mi></math></span>-functions.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"370 ","pages":"Pages 34-49"},"PeriodicalIF":1.0000,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166218X25001325","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/3/14 0:00:00","PubModel":"Epub","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we provide a new proof for the Ihara expression of the alternating -function of a digraph. Furthermore, we present a relation between the weighted alternating -function of a digraph and that of the quotient of its regular covering. As an application, we give a decomposition formula for the weighted alternating zeta function of the quotient of a regular covering of a digraph by its weighted alternating -functions.
期刊介绍：
The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal.
Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.
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