Cubic Graceful Labeling for Star and Bistar Related Graphs (International Journal of Emerging Trends in Science and Technology, 2017)
In this paper we proved some new theorems related with Cubic Graceful Labeling. A graphG(V,E) with nvertices and m edges is said to be a Cubic graceful graph if there exists an injectivefunctionf:V(G)→{0,1,2,3,………m3} such that the induced mappingf:E(G):→{13,23,33,……….m3}defined by f(uv)=|f(u)-f(v)| is an injection the resulting edge labels andvertex labels are distinct. Thefunction f is called a cubic graceful labeling of G. we have proved that thestar K1,n, bistar Bm,n, thegraph obtained by the subdivision of the edges of the star K1,n , the graphobtained by the subdivision of thecentral edge of the bistar Bm,n are cubic graceful graphs