# H-E-Supermagic labelings of some families of graphs

## Abstract

Let $G$ be a simple graph with $p$ vertices and $q$ edges. A simple graph $G$ admits an H-covering in E(G) belongs to a subgraph of $G$ isomorphic to $H$. The graph $G$ is said to be $H$-magic if there exists a bijection $f: V(G) \cup E(G) \rightarrow \{ 1,2 , \ldots, p + q \}$ such that for every subgraph $H^{'}$ of $G$ isomorphic to $H$, $ \sum\limits_{v \in V(H^{'})} f(v) + \sum\limits_{e \in E(H^{'})} f(e) = M$ for some positive integer $M$. $G$ is said to be $H$-$E$-Supermagic if $f(E(G)) = \{ 1,2 , \ldots, q\}$. In this paper we study $H$-$E$-Supermagic labelings of fans, triangle ladders, graphs obtained by joining a star $K_{1,n}$ with one isolated vertex, books and grids.

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## License

Copyright (c) 2024 K. Iyappan, A. Loganathan, Duraisamy Kumar

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

## How to Cite

*Nonlinear Studies*,

*31*(3), 957-963. https://nonlinearstudies.com/index.php/nonlinear/article/view/3709