New families of star-supermagic graphs

Anak Agung Gede Ngurah

Abstract


A simple graph $G$ admits a \textit{$K_{1, n}$-covering} if every
edge in $E(G)$ belongs to a subgraph of $G$ isomorphic to $K_{1, n}$. The
 graph $G$ is $K_{1, n}$-supermagic if there exists  a bijection $f : V(G)
\cup E(G) \rightarrow \{1, 2, 3, \cdots, |V(G) \cup E(G)|\}$ such
that for every subgraph $H'$ of $G$ isomorphic to $K_{1, n}$, $\sum_{v \in
V(H')} f(v) + \sum_{e \in E(H')} f(e)$ is  a constant and $f(V(G)) = \{1, 2, 3, \cdots, |V(G)|\}$. In such a case, $f$ is called a $K_{1, n}$-supermagic labeling of $G$.  In this paper, we give a method how to construct  $K_{1, n}$-supermagic graphs from the old ones.

Keywords


$K_{1, n}$-covering \sep $K_{1, n}$-supermagic labeling \sep $K_{1, n}$-supermagic graph

Full Text:

PDF

DOI: http://dx.doi.org/10.19184/ijc.2020.4.2.4

References

H. Enomoto, A. Llado, T. Nakamigawa, and G. Ringel, Super edge magic graphs, SUT J. Math., 34 (1998), 105–109.

J.A. Gallian, A dynamic survey of graph labelings, Electron. J. Combin., 14 (2019) # DS6.

A. Gutiérrez and A. Lladó, Magic coverings, J. Combin. Math. Combin. Comput., 55 (2005), 43–56.

P. Jeyanthi and P. Selvagopal, Construction of supermagic graphs, Communicated.

A. Kotzig and A. Rosa, Magic valuation of finite graphs, Canad. Math. Bull., Vol. 13 (4), (1970), 451–461.

K.W. Lih, On magic and consecutive labelings of plane graphs, Utilitas Math., 24 (1983), 165–197.

A. Lladó and J. Moragas, Cycle-magic graphs, Discrete math., 307 (23), (2007), 2925–2933.

A.A.G. Ngurah, A.N.M. Salman, and L. Susilowati, H-supermagic labelings of graphs, Discrete Math., 310 (8), 1293–1300.


Refbacks

  • There are currently no refbacks.


ISSN: 2541-2205

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

View IJC Stats