Abstract
A signed graph is a graph whose edges are signed. In a vertex-signed graph the vertices are signed. The latter is called consistent if the product of signs in every circle is positive. The line graph of a signed graph is naturally vertex-signed. Based on a characterization by Acharya, Acharya, and Sinha in 2009, we give constructions for the signed simple graphs whose naturally vertex-signed line graph is consistent.
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Communicated by Xueliang Li.
Dedicated to a great man, Dr. B. Devadas Acharya (1947–2013).
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Zaslavsky, T. Consistency in the Naturally Vertex-Signed Line Graph of a Signed Graph. Bull. Malays. Math. Sci. Soc. 39 (Suppl 1), 307–314 (2016). https://doi.org/10.1007/s40840-015-0281-3
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DOI: https://doi.org/10.1007/s40840-015-0281-3