Geodesic
Characterization of Line-Consistent Signed Graphs
Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 3, pp. 589-594

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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.
Keywords: line-consistent signed graph, line graph, consistent vertex-signed graph, consistent marked graph 
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     title = {Characterization of {Line-Consistent} {Signed} {Graphs}},
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Slilaty, Daniel C.; Zaslavsky, Thomas. Characterization of Line-Consistent Signed Graphs. Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 3, pp. 589-594. http://geodesic.mathdoc.fr/item/DMGT_2015_35_3_a15/