Edge even graceful labelling of some book 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 if there is a bijection f from the edges of the graph to the set $\{2, 4,\ldots , 2q\}$ 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. They proved necessary and sufficient conditions for some path and cycle-related graphs to be edge even graceful. In this paper we proved that triangular book graphs and quadrilateral book graphs admit edge even graceful labelling.

Keywords

• Edge even graceful labelling
• triangular book graphs
• quadrilateral book graphs