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The Scattering Number of Strictly Chordal Graphs: Linear Time Determination

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Abstract

The scattering number of a graph G was defined by Jung in 1978 as \(sc(G) = max \{ \omega (G - S) - |S|, S \subseteq V, \omega (G - S) \ne 1\}\) where \(\omega (G - S) \) is the number of connected components of the graph \(G-S\). It is a measure of vulnerability of a graph and it has a direct relationship with its toughness. Strictly chordal graphs, also known as block duplicate graphs, are a subclass of chordal graphs that includes block and 3-leaf power graphs. In this paper we present a linear time solution for the determination of the scattering number and scattering set of strictly chordal graphs. We show that, although the knowledge of the toughness of the strictly chordal graphs is helpful, it is far from sufficient to provide an immediate result for determining the scattering number.

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Acknowledgements

Partially supported by grant 304706/2017-5, CNPq, Brazil.

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  1. NCE/PPGI - Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brazil

    Lilian Markenzon

  2. IME - Universidade do Estado do Rio de Janeiro, Rio de Janeiro, RJ, Brazil

    Christina F. E. M. Waga

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  1. Lilian Markenzon
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  2. Christina F. E. M. Waga
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Correspondence to Christina F. E. M. Waga.

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Markenzon, L., Waga, C.F.E.M. The Scattering Number of Strictly Chordal Graphs: Linear Time Determination. Graphs and Combinatorics 38, 102 (2022). https://doi.org/10.1007/s00373-022-02498-8

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  • DOI: https://doi.org/10.1007/s00373-022-02498-8

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