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arXiv · 1404.1651

Characterization of Line-Consistent Signed Graphs

Daniel C. Slilaty·Thomas Zaslavsky
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Abstract

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.

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BibTeXRIS

Daniel C. Slilaty, Thomas Zaslavsky. 2015-07-01. Characterization of Line-Consistent Signed Graphs. https://doi.org/10.7151/dmgt.1825

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