A balanced signed digraph
type: Item
instance of: scholarly article
title: A balanced signed digraph
zbMATH Open document ID: 1330.05080
author: Yusuke Higuchi
author: Iwao Sato
published in: Graphs and Combinatorics
publication date: 2015-12-17T00:00:00Z
review text: \textit{F. Harary} [Mich. Math. J. 2, 143--146 (1954; Zbl 0056.42103)] defined a balanced signed graph and presented a necessary and sufficient condition for a signed graph to be balanced. \textit{I. Sato} [Electron. J. Comb. 13, No. 1, Research paper R91, 12 p. (2006; Zbl 1114.05084)] studied a factorization of the weighted zeta function of an (irregular or regular) covering of a graph by equivalence classes of prime, reduced cycles of the base graph, and discussed the structure of balanced covering of signed graphs. Motivated by these results, they extended a balanced signed graph to a digraph, and presented a necessary and sufficient condition for a signed digraph to be balanced. Furthermore, they given another characterization for a signed digraph \((D, w)\) to be balanced by using the weighted Ihrar zeta function and the Ihara zeta function of \(D\). At the end, authors studied the structure of balanced covering of a digraph. This paper is worth reading. It will useful to researcher on signed graph .
reviewed by: V. Lokesha
Mathematics Subject Classification ID: 05C22
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 05C40
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 11M99
zbMATH DE Number: 6521736
zbMATH Keywords: balanced signed digraph
zbMATH Keywords: strongly connectivity
zbMATH Keywords: covering
zbMATH Keywords: zeta function
MaRDI profile type: Publication
full work available at URL: s00373-014-1496-z
OpenAlex ID: W1979199791
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DOI: 10.1007/S00373-014-1496-Z
description: scientific article; zbMATH DE number 6521736