Abstract: A signed graph (marked graph) is an ordered pairwhereis a graph called the underlying graph of Sand is a function. The triangular line graph of a graph is a graph with vertex set such that two vertices eand fare
adjacent if and only if the corresponding edges in Gbelong to a triangle of G. Analogously, we define the triangular line signed graph of a signed graph asa signed graph where is the underlying graph of where for any edge in It is shown that for any signed
graph S, its triangular line signed graph is balanced. Two signed graphs and are switching equivalent written whenever there exists a marking mof such that the signed graph obtained by changing the sign of
everyedgeofto its opposite whenever its end vertices are of opposite
signs, is isomorphic to Further, a structural
characterization of signed graphs that are switching equivalent to their line
signed graphs is obtained.
Keywords and phrases: signed graphs, balance, switching, triangular line signed graph, line signed graph.
