Edge odd graceful labeling of some path and cycle related graphs

Peer review under responsibility of Kalasalingam University.

Abstract

Solairaju and Chithra introduced a new type of labeling of a graph $G$ with $p$ vertices and $q$ edges called an edge odd graceful labeling if there is a bijection $f$ from the edges of the graph to the set $\{1,3,\dots ,2q-1\}$ such that, when each vertex is assigned the sum of all edges incident to it $mod2k$, where $k=max(p,q)$, the resulting vertex labels are distinct. In this paper we proved necessary and sufficient conditions for some path and cycle related graphs to be edge odd graceful such as: Friendship graphs, Wheel graph, Helm graph, Web graph, Double wheel graph, Gear graph, Fan graph, Double fan graph and Polar grid graph.

Keywords:

• Edge odd graceful labeling
• Friendship graph
• Wheel graph
• Double fan graph
• Polar grid graph

Notes

Peer review under responsibility of Kalasalingam University.