×

Generalized edge-magic total labellings of models from researching networks. (English) Zbl 1354.05118

Summary: Graph labellings have been used in many applications, such as in the development of redundant arrays of independent disks which incorporate redundancy utilizing erasure codes, some algorithms, design of highly accurate optical gauging systems for use on automatic drilling machines, design of angular synchronization codes, design of optimal component layouts for certain circuit-board geometries, and determining configurations of simple resistor networks which can be used to supply any of a specified set of resistance values. Since some growing graphs were employed successively as models of researching scale-free networks, hierarchical networks and self-similar networks, so we, in this article, will define a new graph labelling and construct network models that admit the new labellings.

MSC:

05C78 Graph labelling (graceful graphs, bandwidth, etc.)
05C82 Small world graphs, complex networks (graph-theoretic aspects)
05C90 Applications of graph theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Baca, M.; Bertault, F.; MacDougall, J.; Miller, M.; Simanjuntak, R.; Slamin, Vertex-antimagic total labelings of graphs, Discuss. Math. Graph Theory, 23, 67-83 (2003) · Zbl 1054.05086
[3] Bondy, J. A.; Murty, U. S.R., Graph Theory (2008), Springer, ISBN: 978-1-84628-969-9, e-ISBN: 978-1-84628-970-5. http://dx.doi.org/10.1007/978-1-84628-970-5 · Zbl 1134.05001
[4] Chen, Yen-Liang; Chiu, Yu-Ting, Vector space model for patent documents with hierarchical class labels, J. Inform. Sci., 38, 222-233 (2012), First published on March 15, 2012. http://dx.doi.org/10.1177/0165551512437635
[5] Daoud, Mariam; Tamine, Lynda; Boughanem, Mohand, A personalized search using a semantic distance measure in a graph-based ranking model, J. Inform. Sci., 37, 614-636 (2011), December, first published on November 14, 2011. http://dx.doi.org/10.1177/0165551511420220
[6] Gallian, Joseph A., A dynamic survey of graph labelling, Electron. J. Combinator., 14, DS6 (2010) · Zbl 0953.05067
[7] Khosravi-Farsani, Hadi; Nematbakhsh, Mohammadali; Lausen, Georg, SRank, shortest paths as distance between nodes of a graph with application to RDF clustering, J. Inform. Sci., 39, 198-210 (2013), First published on November 8, 2012. http://dx.doi.org/10.1177/0165551512463994
[8] Kotzig, A.; Rosa, A., Magic valuations of finite graphs, Can. Math. Bull., 13, 451-461 (1970) · Zbl 0213.26203
[9] MacDougall, J. A.; Miller, M.; Slamin; Wallis, W. D., Vertex-magic total labelings of graphs, Utilitas Math., 61, 3-21 (2002) · Zbl 1008.05135
[10] Müller, M.; Adachi, T.; Jimbo, M., Cluttered orderings for the complete bipartite graph, Discr. Appl. Math., 152, 213-228 (2005) · Zbl 1080.05083
[11] Newman, M. E.J., Resource letter CS-1: complex systems, Am. J. Phys., 79, 8, 800-810 (2011)
[12] Wallis, W. D., Magic Graphs (2001), Birkhäuser: Birkhäuser Boston · Zbl 0979.05001
[14] Yao, Bing; Cheng, Hui; Yao, Ming; Zhao, Meimei, A note on strongly graceful trees, Ars Combinator., 92, 155-169 (2009) · Zbl 1224.05474
[15] Zhou, Xiangqian; Yao, Bing; Chen, Xiang’en; Tao, Haixia, A proof to the odd-gracefulness of all lobsters, Ars Combinator., 103, 13-18 (2012) · Zbl 1265.05558
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.