New classes of reverse super edge magic graphs

Abstract

A reverse edge magic (REM) labeling of a graph $ G(V, E) $ with $ p $ vertices and $ q $ edges is a bijection $ f:V\left(G \right)\cup E\left(G \right)\to \{1, 2, \cdot \cdot \cdot, p+q\} $ such that $ k = f\left(uv \right)-\{f\left(u \right)+f\left(v \right)\} $ is a constant $ k $ for any edge $ uv\in E\left(G \right). $ A REM labeling $ f $ is called reverse super edge magic (RSEM) labeling if $ f(V(G)) = \; \{1, 2, 3, 4, 5, \ldots, v\} $ and $ f(E(G)) = \{v+1, v+2, v+3, v+4, v+5, \ldots, v+e\}. $ In this paper, we find some new classes of RSEM labeling and the investigation of the connection between the RSEM labeling and different classes of labeling.

Keywords

• trees
• lobster
• banana graph
• cartesian product
• cycle