Cycle with parallel chords are odd even graceful

Abstract

If C_n is a cycle of length n, then the graph cycle with parallel chords is obtained from C_n by adding an “edge between the non adjacent vertices of” C_(n.) Crown C_n□K_1 “is the graph obtained by attaching a pendant edge at each vertex of the cycle” C_(n.) In this paper we prove that the graphs n-cycle with parallel chords for n≥6 and the crowns, C_n□K_(1,) for n≡0,3(mod 4). the graph P_(a,b) obtained by identifying the end points of a internally disjoint paths each of length b, are odd even graceful for odd values of a and b.