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Average distance, surface area, and other structural properties of exchanged hypercubes

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Abstract

Exchanged hypercubes (Loh et al. in IEEE Trans Parallel Distrib Syst 16:866–874, 2005) are spanning subgraphs of hypercubes with about one half of their edges but still with many desirable properties of hypercubes. In this paper, it is shown that distance properties of exchanged hypercubes are also comparable to the corresponding properties of hypercubes. The average distance and the surface area of exchanged hypercubes are computed and it is shown that exchanged hypercubes have asymptotically the same average distance as hypercubes. Several additional metric and other properties are also deduced and it is proved that exchanged hypercubes are prime with respect to the Cartesian product of graphs.

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Acknowledgments

We would like to thank the anonymous referees for their helpful comments and suggestions. This work was supported in part by ARRS Slovenia under the grant P1-0297, the China-Slovenia bilateral grant BI-CN/11-13-001, and the national natural science foundation of China 11101378.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia

    Sandi Klavžar

  2. Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia

    Sandi Klavžar

  3. Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia

    Sandi Klavžar

  4. Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang , 321004, China

    Meijie Ma

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  1. Sandi Klavžar
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  2. Meijie Ma
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Correspondence to Sandi Klavžar.

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Klavžar, S., Ma, M. Average distance, surface area, and other structural properties of exchanged hypercubes. J Supercomput 69, 306–317 (2014). https://doi.org/10.1007/s11227-014-1153-6

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