Signed labeled graph

Signed labeled graph --- знаковый помеченный граф.

A graph [math]\displaystyle{ G }[/math] is said to be signed if each edge of [math]\displaystyle{ G }[/math] is given an odd or even label. In a signed graph [math]\displaystyle{ G }[/math], a subset of [math]\displaystyle{ E(G) }[/math] is odd (resp., even) if it contains an odd (resp. even) number of odd-labeled edges. A graph is odd-signable, if it can be signed so that the edge set of every chordless cycle is odd. A signed graph is odd-signed, if the edge set of every chordless cycle is odd. A signed graph [math]\displaystyle{ S }[/math] is balanced, if every cycle in [math]\displaystyle{ S }[/math] is positive.