A new graceful labeling for pendant graphs

Abstract

A graceful labeling of a graph G with q edges is an injective assignment of labels from {0, 1,..., q} to the vertices of G so that when each edge is assigned the absolute value of the difference of the vertex labels it connects, the resulting edge labels are distinct. A labeling of the first kind for coronas CnȮ K1 occurs when vertex labels 0 and q = 2n are assigned to adjacent vertices of the n-gon. A labeling of the second kind occurs when q = 2n is assigned to a pendant vertex. Previous research has shown that all coronas CnȮ K1 have a graceful labeling of the second kind. In this paper we show that all coronas CnȮ K1 with n ≡ 3,4 (mod 8) also have a graceful labeling of the first kind. © 2013 The Author(s).