Edge even graceful labelling of new families of graphs

Abstract

Elsonbaty and Daoud introduced a new type of labelling of a graph G with p vertices and q edges called an edge even graceful labelling. A graph G is called edge even graceful if there is a bijection $f: E(G) \rightarrow \{2, 4,\ldots , 2q\} $ such that, when each vertex is assigned the sum of all edges incident to it mod $2k $, where $k = \max (p,q ) $, the resulting vertex labels are distinct. In this paper we proved that double fan graphs, quadrilateral friendship graphs, and butterfly graphs are edge even graceful graphs.

Keywords

• edge even graceful labelling
• double fan graph
• friendship graph
• butterfly graph