$H$-$V$-super magic decomposition of complete bipartite graphs
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
An $H$-magic labeling in a $H$-decomposable graph $G$ is a bijection $ f: V(G)\cup E(G)\rightarrow {\{1,2, \ldots ,p+q\}}$ such that for every copy $H$ in the decomposition, $ \sum_{v\in V(H)} f(v)+\sum_{e\in E(H)} f(e)$ is constant. $f$ is said to be $H$-$V$-super magic if $f(V(G))={\{1,2, \ldots ,p\}}$. In this paper, we prove that complete bipartite graphs $K_{n,n}$ are $H$-$V$-super magic decomposable where $ H\cong K_{1,n} $ with $n\geq1$.
Abstract
An $H$-magic labeling in a $H$-decomposable graph $G$ is a bijection $ f: V(G)\cup E(G)\rightarrow {\{1,2, \ldots ,p+q\}}$ such that for every copy $H$ in the decomposition, $ \sum_{v\in V(H)} f(v)+\sum_{e\in E(H)} f(e)$ is constant. $f$ is said to be $H$-$V$-super magic if $f(V(G))={\{1,2, \ldots ,p\}}$. In this paper, we prove that complete bipartite graphs $K_{n,n}$ are $H$-$V$-super magic decomposable where $ H\cong K_{1,n} $ with $n\geq1$.
참고문헌 (22)
- J. Akiyama, "Path Factors of a Graph, Graphs and Applications" (1985), Wiley
- G. Chartrand, "Graphs and Digraphs" (1996), Chapman and Hall
- G. Chartrand, "Chromatic Graph Theory" (2009), Chapman and Hall, CRC
- Y. Egawa, "A decomposition of complete bipartite graphs into edge-disjoint subgraphs with star components", Discrete Math, 58(1), pp.93~95 (1986)
- H. Emonoto, "Super edge-magic graphs", SUT J. Math, 34, pp.105~109 (1998)
- J. A. Gallian, "A dynamic survey of graph labeling", Electron. J. Combin, 16 (2013)
- A. Guti´errez, "Magic coverings", J. Combin. Math. Combin. Comput, 55, pp.43~56 (2005)
- N. Inayah, "Magic and antimagic H-decompositions", Discrete Math, 312(7), pp.1367~1371 (2012)
- T. Kojima, "On C4-Supermagic labelings of the Cartesian product of paths and graphs", Discrete Math, 313(2), pp.164~173 (2013)
- Z. Liang, "Cycle-supermagic decompositions of complete multipartite graphs", Discrete Math, 312(22), pp.3342~3348 (2012)
- A. Llad´o, "Cycle-magic graphs", Discrete Math, 307(23), pp.2925~2933 (2007)
- J. A. MacDougall, "Vertex-magic total labelings of graphs", Util. Math, 61, pp.3~21 (2002)
- J. A. MacDougall, "Super vertex-magic total labeling of graphs", Proc. 15th AWOCA, pp.222~229 (2004)
- G. Marimuthu, "E-super vertex magic labelings of graphs", Discrete Appl. Math, 160(12), pp.1766~1774 (2012)
- G. Marimuthu, "Super edge magic graceful graphs", Inform. Sci, 287, pp.140~151 (2014)
- A. M. Marr, "Magic Graphs" (2013), Birkhauser
- T. K. Maryati, "On H-Supermagic labeling for certain shackles and amalgamations of a connected graph", Util. Math, 83, pp.333~342 (2010)
- A. A. G. Ngurah, "H-Supermagic labeling of graphs", Discrete Math, 310(8), pp.1293~1300 (2010)
- M. Roswitha, "H-Magic covering on some classes of graphs", AIP Conf. Proc, 1450, pp.135~138 (2012)
- J. Sedlacek, "Problem 27, Theory of Graphs and its Applications", Proceedings of Symposium Smolenice, pp.163~167 (1963)
- K. A. Sugeng, "Construction of Super edge magic total graphs", Proc. 16th AWOCA, pp.303~310 (2005)
- T.-M. Wang, "Note on E-super vertex magic graphs", Discrete Appl. Math, 178, pp.160~162 (2014)