Abstract

In this paper we proved some new theorems related with Cubic Graceful Labeling. A graphG(V,E) with n
vertices and m edges is said to be a Cubic graceful graph if there exists an injective
functionf:V(G)→{0,1,2,3,………m3
} such that the induced mapping
f:E(G):→{13
,23
,33
,……….m3
}defined by f(uv)=|f(u)-f(v)| is an injection the resulting edge labels and
vertex labels are distinct. Thefunction f is called a cubic graceful labeling of G. we have proved that the
star K1,n, bistar Bm,n, thegraph obtained by the subdivision of the edges of the star K1,n , the graph
obtained by the subdivision of thecentral edge of the bistar Bm,n are cubic graceful graphs