Induced magic labeling of some graphs
Authors :
K.B. Libeeshkumar 1 * and V. Anil Kumar 2
Author Address :
1,2 Department of Mathematics University of Calicut, Malappuram, Kerala-670007, India.
*Corresponding author.
Abstract :
Let $G=(V ,E )$ be a graph and let $(A,+)$ be an Abelian group with identity element$0.$ Let $f: V \rightarrow A $ be a vertex labeling and $f^{*}: E \rightarrow A$ be the induced labeling of $f,$ defined by $f^* (v_1v_2)=f(v_1)+f(v_2)$ for all $v_1v_2\in E .$ Then $f^*$ again induces a labeling say $f^{**}: V \rightarrow A$ defined by $\displaystyle{f^{**}(v)=\sum_{vv_1\in E}} f^*(vv_1).$ A graph $G=(V ,E )$ is said to be an Induced $A$-Magic Graph (IAMG) if there exists a non zero labeling $f: V \rightarrow A $ such that $f\equiv f^{**}.$ The function $f,$ so obtained is called an Induced $A$-Magic Labeling (IAML) of $G$ and a graph which has no such Induced Magic Labeling is called a Non-induced magic graph. In this paper we discuss the existence of Induced Magic Labeling of some special graphs like $P_n,\ C_n,\ K_n$ and $K_{m,n}.$}
Keywords :
Induced $A$-Magic Labeling of Graphs, Induced $A$-Magic graphs.
DOI :
Article Info :
Received : October 11, 2019; Accepted : December 27, 2019.
