Super total graceful labeling of some trees

Abstract

A graph labeling is an assignment of integers to the edges, vertices, or both of a graph so that it meets to certain conditions. A graph labeling is called total labeling if labeling is given to edges and vertices. Let G be a simple and finite graph having vertex set V(G), edge set E(G), number of vertices p, and number of edges q. A super total graceful labeling of G is a bijection f from V(G) ∪ E(G) to the set {1,2,3,….,p + q} such that f(uv) = |f(u) – f(v)| for every uv ∈ E(G) and f(E(G)) = {1,2,3,…, q}. A graph that admits a super total graceful labeling is called a super total graceful graph. In this paper we show that star graph K 1,n , spider graph SP(1 n , 2 m ), and caterpillar graph P 3⨀nK 1 are super total graceful graphs.