Construction of Line-Consistent Signed Graphs
نویسنده
چکیده
The line graph of an edge-signed graph 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 edge-signed graphs whose line graphs are consistent. Their proof applies Hoede’s relatively difficult characterization of consistent vertex-signed graphs. We give a different, constructive proof that does not depend on Hoede’s theorem. Mathematics Subject Classifications (2010): Primary 05C22; Secondary 05C76.
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