Some Special $V_4$-magic Graphs

Abstract

For any abelian group $A$, a graph $G=(V,E)$ is said to be
$A$-magic if there exists a labeling $l:E(G)\to A-\{0\}$ such that the induced vertex set labeling $l^+:V(G)\to A$ defined by $l^+ :=\sum\{l({\it uv})/{\it uv}\in E(G)\}$ is a constant map. In this paper, we consider the Klein-four group $V_4=Z_2\oplus Z_2$ and investigate graphs that are $V_4$-magic.