Graceful labeling on twig diamond graph with pendant edges

Abstract

A graceful labeling of a graph $G$ with $q$ edges is an injection $f: V(G) \to \{0,1,2,\ldots,q\}$  with the property that the resulting edges are also distinct, where an edge incident with the vertices $ u$} and $ v$ is assigned the label $|f(u) - f(v)|$. A graph which admits a graceful labeling is called a graceful graph. In this paper, we prove the graceful labeling of a new family of graphs $G$ called a twig diamond graph with pendant edges.