Point signed and line signed graphs (Q800942)

A graph G is p-signed (l-signed) if every point (line) is signed either positive or negative. A pl-signed graph is both p-signed and l-signed. A p-signed graph G is p-balanced if no component of G contains an odd number of negative points. An l-signed graph G is l-balanced if no cycle of G contains an odd number of negative lines. A pl-signed graph G is pl- balanced if (i) it is both p-balanced and l-balanced, and (ii) the sign of any point u in G is equal to the product of the lines incident with u. We obtain characterizations of p-balanced and pl-balanced graphs. The reader should also see [\textit{B. D. Acharya}, A characterization of consistent marked graphs, Nat. Acad. Sci. Lett. 6, 433-440 (1983)] for a characterization of \(\ell\)-balanced, \(\ell\)-signed graphs.