Restricted super line signed graphRL r (S)

A signed graph (marked graph) is an ordered pair S = (G; ) (S = (G; )), where G = (V;E) is a graph called the underlying graph of S and : E!f+;g ( : V !f+;g ) is a function. The restricted super line graph of index r of a graph G, denoted byRLr(G). The vertices ofRLr(G) are the r-subsets of E(G) and two vertices P = fp1;p2;:::;prg and Q = fq1;q2;:::;qrg are adjacent if there exists exactly one pair of edges, say pi and qj, where 1 i;j r, that are adjacent edges inG. Analogously, one can define the restricted super line signed graph of indexr of a signed graph S = (G; ) as a signed graphRLr(S) = (RLr(G); 0 ), whereRLr(G) is the underlying graph ofRLr(S), where for any edge PQ inRLr(S), 0 (PQ) = (P) (Q). It is shown that for any signed graph S, itsRLr(S) is balanced and we offer a structural characterization of restricted super line signed graphs of indexr. Further, we characterize signed graphsS for whichRLr(S)L r(S) andRLr(S) =Lr(S), where and = denotes switching equivalence and isomorphism andRLr(S) andLr(S) are denotes the restricted super line signed graph of indexr and super line signed graph of indexr of