Some Difference Graphs

Abstract

In this paper, we discuss difference labeling of some standard families of graphs. We prove that Star, Butterfly, Bistar, umbrella and Olive tree are difference graphs. We also introduce difference labelings for some snakes (double triangular snake, irregular triangular snake, alternate $C_n$ snake). Furthermore we introduce a corollary helps us to find a unique difference labeling for the complete graph $K_3$ and all forms of difference labeling for the Star graph. Also this corollary can be used to prove that the complete bipartite graph $K_{2,4}$ is not a difference graph but the proof is very lengthy.