On the Q(a)P(b)-Super Edge-Graceful (p,P+I)-Graphs

Let a and b be two positive integers. For the graph G with vertex set V(G) and edge set E(G) with p=IV(G)1 and q=IE(G)I, we define two sets Q(a) and PCb) as follows: Q(a) ={ ± a, ± (a+ 1), ... , ±(a +(q-2)12)} if q is even, Q(a) = (O} u( ± a, ± (a+ 1), ... , ±(a +(q-3)12)} if q is odd, PCb) ={ ± b, ± (b+ I), ... , ±(b +(p-2)/2) l if p is even, PCb) {Ol u( ±b,±(b+l), ... ,±(b+(p-3)12)} ifpisodd. For the graph G with p=IV(G)1 and q=IE(G)I, G is said to be JCMCC 62 (2007), pp. 193-216 Q(a)P(b)-super edge-graceful (in short Q(a)P(b)-SEO). if there exists a function pair (f, n which assigns integer labels to the vertices and edges; that is, f": V (0) ~ P(b), and f: E (0) ~Q(a) such that f" is onto P(b) and fis onto Q(a). and f"(u) = E{f(u,v): (u. v) E E (0) }. We investigate Q(a)P(b) super-edge-gracefullabelings for three classes of (p,P+ 1)graphs.