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Group magicness of certain planar graphs | ||
| Transactions on Combinatorics | ||
| مقاله 1، دوره 3، شماره 2، شهریور 2014، صفحه 1-9 اصل مقاله (151.55 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2014.4268 | ||
| نویسندگان | ||
| Mohammad Javad Nikmehr* 1؛ Samaneh Bahramian2 | ||
| 1K.N.Toosi University | ||
| 2Department of Mathematics, Karaj Branch, Islamic Azad Uneversity, Karaj-Iran | ||
| چکیده | ||
| Let $A$ be a non-trivial abelian group and $A^{*}=A\setminus \{0\}$. A graph $G$ is said to be $A$-magic graph if there exists a labeling $l:E(G)\rightarrow A^{*}$ such that the induced vertex labeling $l^{+}:V(G)\rightarrow A$, define by $$l^+(v)=\sum_{uv\in E(G)} l(uv)$$ is a constant map. The set of all constant integers such that $\sum_{u\in N(v)} l(uv)=c$, for each $v\in N(v)$, where $N(v)$ denotes the set of adjacent vertices to vertex $v$ in $G$, is called the index set of $G$ and denoted by ${\rm In}_{A}(G).$ In this paper we determine the index set of certain planar graphs for $\mathbb{Z}_{h}$, where $h\in \mathbb{N}$, such as wheels and fans. | ||
| کلیدواژهها | ||
| Index Set؛ Magic؛ Zero-Sum؛ Null Set | ||
| مراجع | ||
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Combin. 82, 41-53
E. Salehi (2006) Integer-magic spectra of cycle related
graphs Iranian J. Math. Sci Inform 1 (2), 53-63
E. Salehi and S. Hansen (2010) Zero sum magic and null
sets of planar graphs J. Combin. Math. Combin. Comput. 72, 55-64
E. Salehi (2008) On zero-sum magic graphs and their null
sets Bull. Inst. Math. Acad. Sin. (N.S.) 3, 255-264
J. Sedlacek (1976) On magic graphs Math. Slovaca 26, 329-335
J. Sedlacek (1976) Some properties of magic graphs, in Graphs, Hypergraph, and Bloc Syst Proc. Symp. Comb. Anal,
Zielona Gora , 247-253
T.-M. Wang and S.-W. Hu (2011) Constant sum flows in regular graphs Lecture Notes in Computer Science 6681, 168-175
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