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.
@article{bwmeta1.element.doi-10_7151_dmgt_1825,
author = {Daniel C. Slilaty and Thomas Zaslavsky},
title = {Characterization of Line-Consistent Signed Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {35},
year = {2015},
pages = {589-594},
zbl = {1317.05081},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1825}
}
Daniel C. Slilaty; Thomas Zaslavsky. Characterization of Line-Consistent Signed Graphs. Discussiones Mathematicae Graph Theory, Tome 35 (2015) pp. 589-594. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1825/
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