The K-gracefulness On The Subdivision Graph Of A Class Of Column Graph

Graceful graph is one of the most interesting research topic in graph theory, the inter-est and the use of it, from60time metaphase was put forward, has gained in importance.For an undirected simple graph G=(V, E),If for each point v∈V, The existence of a nonnegative integer f(v), So as to satisfy the condition:(1)(?)v, v∈E V,if u≠v,then∫(u)≠∫(v);(2)max{f(v)|v∈V}=|E|;(3)(?)e1,e2∈E,if e1≠e2,then f’(e1)≠f’(e2);in which f’(e)=|f(u)-f(v)|, e=uv,Graph G is graceful graph,Gis called f graceful value,or graceful labeling.Graceful graph is widely used in radio astronomy, X-ray crystallography, X cryp-tography, communication network for field access, circuit design, the design, the whole voltage generator missile control code design, code design of synchronous machine.Let G be a simple graph, if one vertex is put between every two adjacent vertexes of G,then the produced graph is called a subdivision graph of G.In this paper, we verify the k-gracefulness on the subdivision graph of the produce graphs Cλ(Pn) and Cλ(Cn).