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

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^′, E^′) be a connected graph. 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 ⊳_o H, is a graph obtained by taking a copy of graph 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 H₁ ⊳_o H₂-supermagic labeling of graph G ⊳_o H₂ where G is H₁-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.

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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  -