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Graph Products and Configuration Processing

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Optimal Analysis of Structures by Concepts of Symmetry and Regularity

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Abstract

Graph products are defined and developed in the past 50 years (see, e.g. Berge [1], Sabidussi [2], Harary and Wilcox [3]). An excellent book covering the mathematics of graph products is that of Imrich and Klavzar [4]. In this chapter, the necessary definitions from graph products are presented and examples are included to illustrate the definitions pictorially. The number of graph products in literature is far more than four; however, products which have extensively been studied in mathematics are as follows:

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References

  1. Berge C (1973) Graphs and hypergraphs. North-Holland, Amsterdam

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  2. Sabidussi G (1960) Graph multiplication. Math Zeit 72:446–457

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  3. Harary F, Wilcox GW (1967) Boolean operations on graphs. Math Scand 20:41–51

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  4. Imrich W, Klavžar S (2000) Product graphs; structure and recognition. Wiley, New York

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  5. Kaveh A, Koohestani K (2008) Graph products for configuration processing of space structures. Comput Struct 86:1219–1236

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  7. Kaveh A, Beheshti S (2012) Weighted triangular and circular graph products for configuration processing. Period Polytech-Civil Eng 56(1):1–9

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  8. Kaveh A, Beheshti S (2013) New graph products for configuration processing. Int J Civil Eng 11(2):67–76

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Authors and Affiliations

  1. Centre of Excellence for Fundamental Studies in Structural Engineering Department of Civil Engineering, Iran University of Science and Technology, Tehran, Iran

    A. Kaveh

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  1. A. Kaveh
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© 2013 Springer-Verlag Wien

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Kaveh, A. (2013). Graph Products and Configuration Processing. In: Optimal Analysis of Structures by Concepts of Symmetry and Regularity. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1565-7_3

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  • DOI: https://doi.org/10.1007/978-3-7091-1565-7_3

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  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-1564-0

  • Online ISBN: 978-3-7091-1565-7

  • eBook Packages: EngineeringEngineering (R0)

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