Zk-Magic labeling of subdivision graphs

Abstract

For any nontrivial abelian group [Formula: see text] under addition a graph [Formula: see text] is said to be [Formula: see text]-magic if there exists a labeling [Formula: see text] such that the vertex labeling [Formula: see text] defined as [Formula: see text] taken over all edges [Formula: see text] incident at [Formula: see text] is a constant. An [Formula: see text]-magic graph [Formula: see text] is said to be [Formula: see text]-magic graph if the group [Formula: see text] is [Formula: see text] the group of integers modulo [Formula: see text]. These [Formula: see text]-magic graphs are referred to as [Formula: see text]-magic graphs. In this paper, we prove that the graphs such as subdivision of ladder, triangular ladder, shadow, total, flower, generalized prism, [Formula: see text]-snake, lotus inside a circle, square, gear, closed helm and antiprism are [Formula: see text]-magic graphs. Also we prove that if [Formula: see text] be [Formula: see text]-magic graphs with magic constant zero then [Formula: see text] is also [Formula: see text]-magic.