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On Domination and Independence Numbers of Graphs

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A set S of vertices of a graph G is dominating if each vertex x not in S is adjacent to some vertex in S, and is independent if no two vertices in S are adjacent. The domination number, γ(G), is the order of the smallest dominating set in G. The independence number, α(G), is the order of the largest independent set in G. In this paper we characterize bipartite graphs and block graphs G for which γ(G) = α(G).

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Authors and Affiliations

  1. Lehrstuhl II für Mathematik, Rheinisch-Westfälische Technische Hochschule Aachen, Templergraben 55, D-5100, Aachen, Germany

    Jerzy Topp & Lutz Volkmann

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  1. Jerzy Topp
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  2. Lutz Volkmann
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On leave from the Faculty of Applied Physics and Mathematics, Gdańsk Technical University, 11/12 Majakowskiego, 80-952 Gdańsk, Poland. Research supported by the Heinrich Herts Foundation.

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Topp, J., Volkmann, L. On Domination and Independence Numbers of Graphs. Results. Math. 17, 333–341 (1990). https://doi.org/10.1007/BF03322468

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  • DOI: https://doi.org/10.1007/BF03322468

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