Induced magic labeling of some graphs

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DOI:

https://doi.org/10.26637/MJM0801/0011

Abstract

Let $G=(V, E)$ be a graph and let $(A,+)$ be an Abelian group with identity elemento. Let $f: V \rightarrow A$ be a vertex labeling and $f^*: E \rightarrow A$ be the induced labeling of $f$, defined by $f^*\left(v_1 v_2\right)=f\left(v_1\right)+f\left(v_2\right)$ for all $v_1 v_2 \in E$. Then $f^*$ again induces a labeling say $f^{* *}: V \rightarrow A$ defined by $f^{* *}(v)=\sum_{v v_1 \in E} f^*\left(v v_1\right)$. 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.

Mathematics Subject Classification:

Mathematics
  • K.B. Libeeshkumar Department of Mathematics University of Calicut, Malappuram, Kerala-670007, India.
  • V. Anil Kumar Department of Mathematics University of Calicut, Malappuram, Kerala-670007, India.
  • Pages: 59-61
  • Date Published: 01-01-2020
  • Vol. 8 No. 01 (2020): Malaya Journal of Matematik (MJM)

R. Balakrishnan and K. Ranganathan, A Textbook of Graph Theory, Springer, 2012.

F. Harary, Graph Theory, Addison-Wesley, Reading, MA, 1972.

Chartrand G, Zhang P, Introduction to Graph Theory, McGraw-Hill, Boston; 2005.

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Published

01-01-2020

How to Cite

K.B. Libeeshkumar, and V. Anil Kumar. “Induced Magic Labeling of Some Graphs”. Malaya Journal of Matematik, vol. 8, no. 01, Jan. 2020, pp. 59-61, doi:10.26637/MJM0801/0011.