On Mod(2)-Edge-Magic Graphs

Abstract

Let $G$ be a $(p,q)$-graph where each edge of $G$ is labeled by a number $1,2,\dots ,q$ without repetition. The vertex sum for a vertex $v$ is the sum of the labels of edges that are incident to $v$. If the vertex sums are equal to a constant (mod $k$) where $k\ge 2$, then $G$ is said to be Mod($k$)-edge-magic. In this paper, we investigate graphs which are Mod($k$)-edge-magic. When $k=p$, the corresponding Mod($p$)-edge-magic graph is the edge-magic graph introduced by Lee (third author), Seah, and Tan in $[10]$. In this work, we investigate trees, unicyclic graphs, and $(p,p+1)$-graphs which are Mod(2)-edge-magic.