Characterization of signed line digraphs

Abstract Given a signed digraph S = ( V ( D ) , A ( D ) , σ ) on a given digraph D = ( V , A ) called the underlying digraph of S , its signed line digraph L ( S ) is a signed digraph defined on the line digraph L ( D ) of D by defining an arc e f in it to be negative if and only if both the arcs e and f in S are negative and oriented in the same direction through their common vertex. In this paper, we define a given signed digraph S to be a signed line digraph if there exists a signed digraph H such that L ( H ) ≅ S (read as “ L ( H ) is isomorphic to S ”). We derive three structural characterizations of signed line digraphs, extending the well known characterization of line digraphs due to Hemminger (1972) [10] .