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Deriving formulas for domination numbers of fasciagraphs and rotagraphs

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Book cover Fundamentals of Computation Theory (FCT 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1684))

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Abstract

Recently, an algebraic approach which can be used to compute distance-based graph invariants on fasciagraphs and rotagraphs was given in [Mohar, Juvan, Žerovnik, Discrete Appl. Math. 80 (1997) 57–71]. Here we give an analogous method which can be employed for deriving formulas for the domination number of fasciagraphs and rotagraphs. In other words, it computes the domination numbers of these graphs in constant time, i.e. in time which depends only on the size and structure of a monograph and is independent of the number of monographs. Some further generalizations of the method are discussed, in particular the computation of the independent number and the k-coloring decision problem. Examples of fasciagraphs and rotagraphs include complete grid graphs. Grid graphs are one of the most frequently used model of processor interconnections in multiprocessor VLSI systems.

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This work was partially supported by the Ministry of Science and Technology of Slovenia under the grant J2-1015.

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Author information

Authors and Affiliations

  1. Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, SI-2000, Maribor, Slovenia

    Janez Žerovnik

  2. Department of Theoretical Computer Science, Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1111, Ljubljana, Slovenia

    Janez Žerovnik

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  1. Janez Žerovnik
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Editors and Affiliations

  1. Faculty of Computer Science, “A.I.Cuza” University, 6600, Iaşi, Romania

    Gabriel Ciobanu

  2. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700, Bucharest, Romania

    Gheorghe Păun

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© 1999 Springer-Verlag Berlin Heidelberg

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Žerovnik, J. (1999). Deriving formulas for domination numbers of fasciagraphs and rotagraphs. In: Ciobanu, G., Păun, G. (eds) Fundamentals of Computation Theory. FCT 1999. Lecture Notes in Computer Science, vol 1684. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48321-7_47

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  • DOI: https://doi.org/10.1007/3-540-48321-7_47

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  • Print ISBN: 978-3-540-66412-3

  • Online ISBN: 978-3-540-48321-2

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