Cubic Graceful Labeling for Star and Bistar Related Graphs - Mathew Varkey T.K , Mini.S.Thomas (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 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