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Extremal Singular Graphs

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Discrete Mathematics and Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 165))

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Abstract

A graph is called singular if its adjacency matrix is singular. The problem of characterizing all singular graphs was posed in 1957 by L. Collatz and U. Sinogowitz. Since then, it has been studied intensely due to its great importance in mathematics and in chemistry. However, the problem has proved to be rather complicated and has not yet been solved completely. In this paper, we emphasize on some of the most important results on graphs that are extremal with regard to their nullity/rank.

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Authors and Affiliations

  1. Department of Computer Science, University of Thessaly, Lamia, Greece

    Irene Triantafillou

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  1. Irene Triantafillou
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Editors and Affiliations

  1. Moscow Institute of Physics and Technology, Dolgoprudny, Russia

    Andrei M. Raigorodskii

  2. Institute of Mathematics, University of Zurich, Zurich, Eswatini

    Michael Th. Rassias

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Triantafillou, I. (2020). Extremal Singular Graphs. In: Raigorodskii, A.M., Rassias, M.T. (eds) Discrete Mathematics and Applications. Springer Optimization and Its Applications, vol 165. Springer, Cham. https://doi.org/10.1007/978-3-030-55857-4_20

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