Fibonacci Graceful Graphs

Abstract

In this paper, we introduce two new types of labelings of graphs using Fibonacci numbers, namely, Fibonacci graceful labelings and Super Fibonacci graceful labelings. We discuss the existence and non-existence of Fibonacci and Super Fibonacci graceful labelings for certain classes of graphs. Also, we discuss the Fibonacci gracefulness of disjoint union of Super Fibonacci graceful graphs, pendant edge extension of Super Fibonacci graceful graphs, and amalgamation of Super Fibonacci graceful graphs. Finally, we compare the graceful graphs with Fibonacci graceful graphs.