Graceful labeling of some new graphs

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 edge labels are distinct where the edge incident with the vertices $u$ and $v$ is assigned the label $|f\left(u\right)-f\left(v\right)|$. A graph which admits a graceful labeling is called a graceful graph. In this paper, we prove that the series of isomorphic copies of Star graph connected between two Ladders are graceful.