# Super edge-graceful labelings of total stars and total cycles

For a graph G = (V,E) we associate the total graph T(G) as follows: V (T(G)) = V (G) u E(G) and E(T(G)) = E(G) u { <v, <u,v>> | v in V(G) and <u,v> in E(G) }.

Let [n]* denote the set of integers between -n/2 and n/2. A super edge-graceful labeling f of a graph G of order p and size q is a bijection f : E(G) -> [q]*, such that the induced vertex labeling f* where f*(u) is the sum of f(<u,v>) over all <u,v> in E(G) is a bijection from V (G) to [p]*. A graph is super edge-graceful if it has a super edge-graceful labeling. In this seminar, we first present a brief history of super edge-graceful labelings. Then we prove that the total stars and total cycles are super edge-graceful.