Characterization of Line-Consistent Signed Graphs

Characterization of Line-Consistent Signed Graphs

The line graph of a graph with signed edges carries vertex signs. A vertex-signed graph is consistent if every circle (cycle, circuit) has positive vertex-sign product. Acharya, Acharya, and Sinha recently characterized line-consistent signed graphs, i.e., edge-signed graphs whose line graphs, with...

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Bibliographic Details
Main Authors: Slilaty Daniel C., Zaslavsky Thomas
Format: Article
Language:English
Published: Sciendo 2015-08-01
Series:Discussiones Mathematicae Graph Theory
Subjects:
line-consistent signed graph
line graph
consistent vertex-signed graph
consistent marked graph.
Online Access:https://doi.org/10.7151/dmgt.1825
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spelling doaj-72a51f2935444d1a938de4330a8e392b2021-09-05T17:20:21ZengSciendoDiscussiones Mathematicae Graph Theory2083-58922015-08-0135358959410.7151/dmgt.1825dmgt.1825Characterization of Line-Consistent Signed GraphsSlilaty Daniel C.0Zaslavsky Thomas1Wright State University Dayton, OH 45435-0001, USABinghamton University (SUNY) Binghamton, NY 13902-6000, USAThe line graph of a graph with signed edges carries vertex signs. A vertex-signed graph is consistent if every circle (cycle, circuit) has positive vertex-sign product. Acharya, Acharya, and Sinha recently characterized line-consistent signed graphs, i.e., edge-signed graphs whose line graphs, with the naturally induced vertex signature, are consistent. Their proof applies Hoede’s relatively difficult characterization of consistent vertex-signed graphs. We give a simple proof that does not depend on Hoede’s theorem as well as a structural description of line-consistent signed graphs.https://doi.org/10.7151/dmgt.1825line-consistent signed graphline graphconsistent vertex-signed graphconsistent marked graph.
collection DOAJ
language English
format Article
sources DOAJ
author Slilaty Daniel C.
Zaslavsky Thomas
spellingShingle Slilaty Daniel C.
Zaslavsky Thomas
Characterization of Line-Consistent Signed Graphs
Discussiones Mathematicae Graph Theory
line-consistent signed graph
line graph
consistent vertex-signed graph
consistent marked graph.
author_facet Slilaty Daniel C.
Zaslavsky Thomas
author_sort Slilaty Daniel C.
title Characterization of Line-Consistent Signed Graphs
title_short Characterization of Line-Consistent Signed Graphs
title_full Characterization of Line-Consistent Signed Graphs
title_fullStr Characterization of Line-Consistent Signed Graphs
title_full_unstemmed Characterization of Line-Consistent Signed Graphs
title_sort characterization of line-consistent signed graphs
publisher Sciendo
series Discussiones Mathematicae Graph Theory
issn 2083-5892
publishDate 2015-08-01
description The line graph of a graph with signed edges carries vertex signs. A vertex-signed graph is consistent if every circle (cycle, circuit) has positive vertex-sign product. Acharya, Acharya, and Sinha recently characterized line-consistent signed graphs, i.e., edge-signed graphs whose line graphs, with the naturally induced vertex signature, are consistent. Their proof applies Hoede’s relatively difficult characterization of consistent vertex-signed graphs. We give a simple proof that does not depend on Hoede’s theorem as well as a structural description of line-consistent signed graphs.
topic line-consistent signed graph
line graph
consistent vertex-signed graph
consistent marked graph.
url https://doi.org/10.7151/dmgt.1825
work_keys_str_mv AT slilatydanielc characterizationoflineconsistentsignedgraphs
AT zaslavskythomas characterizationoflineconsistentsignedgraphs
_version_ 1717786515253231616

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