On Square and 2-path Signed Graph.

A signed graph is an ordered pair , where is a graph G = ( V, E), called the underlying graph of S and is a function from the edge set E of Su into the set {+, -}, called the signature of S. In this paper, we characterize all those signed graphs whose 2-path signed graphs are isomorphic to their square signed graph along with algorithm to check the same. In other sections we find the characterization of signed graph S such that where D is a derived signed graph of the signed graph S such as: line signed graphs, total signed graphs, common edge signed graphs, splitting signed graphs. Also each characterization is supported by algorithms for the same. [ABSTRACT FROM AUTHOR]