# Further Result of *H*-Supermagic Labeling for Comb Product of Graphs

^{*}, Aryanto, Meksianis Z. Ndii

^{*}Corresponding author. Email: ganesha.lapenangga@staf.undana.ac.id

- DOI
- 10.2991/acsr.k.220202.007How to use a DOI?
- Keywords
- Comb product; H-supermagic labeling; H-magic
- Abstract
Let

*G*= (*V, E*) and*H*= (*V*) be a connected graph.^{′}, E^{′}*H*-magic labeling of graph*G*is a bijective function*f*:*V*(*G*) ∪*E*(*G*) → {1,2, …, |*V*(*G*)| + |*E*(*G*)|} such that for every subgraph*H*of^{′}*G*isomorphic to*H*,*∑*_{v}_{ }_{∈}_{ V(H′)}*f*(*v*) +*∑*_{e}_{ }_{∈}_{ E(H′)}*f*(*e*) =*k*. Moreover, it is*H*-supermagic labeling if*f*(*V*) = {1,2 ,…, |*V*|}. A graph*G*having such labeling called*H*-supermagic graph. Next, we introduce comb product of graph. Suppose*G*and*H*are two connected graph and*o*is vertex in*H*. A comb product between*G*and*H*, denoted by*G*⊳, is a graph obtained by taking a copy of graph_{o}H*G*and |*V*(*G*)| copies of graph*H*, then identifying the*i*-th copy of graph*H*at vertex*o*to*i*-th vertex of graph*G*. In this paper, we construct*H*_{1}⊳_{o}H_{2}-supermagic labeling of graph*G*⊳_{o}H_{2}where*G*is*H*_{1}-supermagic graph.- Copyright
- © 2022 The Authors. Published by Atlantis Press International B.V.
- Open Access
- This is an open access article under the CC BY-NC license.

### Cite this article

TY - CONF AU - Ganesha Lapenangga P. AU - Aryanto AU - Meksianis Z. Ndii PY - 2022 DA - 2022/02/08 TI - Further Result of H-Supermagic Labeling for Comb Product of Graphs BT - Proceedings of the International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021) PB - Atlantis Press SP - 32 EP - 34 SN - 2352-538X UR - https://doi.org/10.2991/acsr.k.220202.007 DO - 10.2991/acsr.k.220202.007 ID - P.2022 ER -