Characterization of a Signed Graph Whose Signed Line Graph is S-Consistent

A signed graph is a graph in which every edge is designated to be either positive or negative; it is balanced if every cycle contains an even number of negative edges. A marked signed graph is a signed graph each vertex of which is designated to be positive or negative and it is consistent if every cycle in the signed graph possesses an even number of negative vertices. Signed line graph L(S) of a given signed graph S = (G, a), as given by Behzad and Chartrand [7], is the signed graph with the standard line graph L( G) of G as its underlying graph and whose edges are assigned the signs according to the rule: for any eiej E E(L(S)), eiej E E- (L(S))(left right double arrow) the edges ei and ej of 8 are bothnegative in S. Further, L(S) is S-consistent if to each vertex e of L(S), which is an edge of 8, one assigns the sign a(e) then the resulting marked signed graph (L(S))Mu is consistent. In this paper, we give a characterization of signed graphs S whose signed line graphs L(S) are S-consistent.