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Incidence Graphs of Bipartite G-Graphs

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Optimization Theory, Decision Making, and Operations Research Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 31))

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Abstract

Defining graphs from groups is a widely studied area motivated, for example, by communication networks. The most popular graphs defined by a group are Cayley graphs. G-graphs correspond to an alternative construction. After recalling the main properties of these graphs and their motivation, we propose a characterization result. With the help of this result, we show that the incidence graph of a symmetric bipartite G-graph is also a G-graph and we give a proof that, with some constraints, if the incidence graph of a symmetric bipartite graph is G-graph, the graph is also a G-graph. Using these results, we give an alternative proof for the fact that mesh of d-ary trees are G-graphs.

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Author information

Authors and Affiliations

  1. ESSEC Business School, 1 avenue Bernard Hirsch Cergy, Paris, France

    Cerasela Tanasescu

  2. University of Bucharest, Str. Academiei, 14, Bucharest, Romania

    Ruxandra Marinescu-Ghemeci

  3. GREYC CNRS UMR-6072, Université de Caen, Campus II, Bd Marechal Juin, 5186, 14032, Caen cedex, France

    Alain Bretto

Authors
  1. Cerasela Tanasescu
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  2. Ruxandra Marinescu-Ghemeci
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  3. Alain Bretto
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Corresponding author

Correspondence to Cerasela Tanasescu .

Editor information

Editors and Affiliations

  1. , Faculty of Engineering, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece

    Athanasios Migdalas

  2. , Economical and Social Sciences, University of Macedonia, Loggou-Tourpali, Naoussa, 59200, Greece

    Angelo Sifaleras

  3. , Department of Applied Informatics, University of Macedonia, Egnatia St. 156, Thessaloniki, 54006, Greece

    Christos K. Georgiadis

  4. , Department of Marketing and Operations M, University of Macedonia, Agiou Dimitriou 49, Edessa, 58200, Greece

    Jason Papathanasiou

  5. , Department of Applied Informatics, University of Macedonia, Egnatia Street 156, Thessaloniki, 54006, Greece

    Emmanuil Stiakakis

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Tanasescu, C., Marinescu-Ghemeci, R., Bretto, A. (2013). Incidence Graphs of Bipartite G-Graphs. In: Migdalas, A., Sifaleras, A., Georgiadis, C., Papathanasiou, J., Stiakakis, E. (eds) Optimization Theory, Decision Making, and Operations Research Applications. Springer Proceedings in Mathematics & Statistics, vol 31. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5134-1_9

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