SUPER EDGE MAGIC GRACEFUL TOTAL LABELING OF SOME GRAPHS

Abstract

Let a ( , ) p q graph G with the vertex set V G( ) , the edge set E G( ) , the number of vertices is p, and the number of edges is q. The edge magic graceful total labeling of graph G is a bijection from V G E G ( ) ( )  to the integers {1, 2,..., } p q + such that for all edges, the absolute value of the sum of two adjacent vertex labels minus the edge label that connect the two vertexs is a constant k. The super edge magic labeling is edge magic labeling whose the set of vertex labels is {1, 2,..., }p . This final paper shows super edge magic graceful total labeling on path graph ( ) P n , cycle graph ( ) Cn , crown graph ( ) Cn + , and subdivided bistar graph 1, 1, : K K m n . Keywords : Edge magic graceful labeling, super edge magic graceful labeling, path graph, cycle graph, crown graph, subdivided bistar graph.