Graceful and Cordial Labeling Of Subdivision Of Graphs

An edge uv is said to be subdivided if the edge uv   is replaced by the path P:uwvP:uwv, where w is the new vertex. A graph obtained by subdividing each edge of a graph G is called subdivision of the graph G  , and is denoted by S(G)S(G). A shell graph   of size n≥4n≥4, denoted C(n,n−3)C(n,n−3) is the graph obtained from the cycle Cn(v0,v1,v2,⋯,vn−1)Cn(v0,v1,v2,⋯,vn−1) by adding n−3n−3 consecutive chords incident with a common vertex v0v0(say) called apex of the shell graph.In this paper, we show that the graph S(K2,n)S(K2,n) is graceful and cordial, for n≥1n≥1 and the graph S(C(n,n−3))S(C(n,n−3)) is graceful and cordial for n≥4n≥4.