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The structure of threshold graphs

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Abstract

Manca has derived an efficient matrix method for testing a given graph to see whether or not it is a threshold graph.

Chvátal and Hammer introduced these graphs which can be defined by the condition that they do not contain as induced subgraphs 2K2, P4, or C4. Implicit in the results of Manca is a structural description of such graphs. Our object is to display the structure of threshold graphs explicitly by a combination of contraction and homomorphism and the use of the bipartite-adjacency matrix.

Riassunto

L’autore riprende un metodo proposto da P. Manca per stabilire se un dato grafo è un « threshold graph » (secondo la terminologia di Chvátal e Hammer), e si propone di porre in evidenza la struttura di questa varietà di grafi facendo ricorso ad una combinazione di contrazioni e omomorfismi e all’uso di una « bipartite-adjacency-matrix ».

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References

  1. R. Brualdi, F. Harary, Z. Miller,Bigraphs versus digraphs via matrices. J. Graph Theory, to appear.

  2. V. Chvátal, P. L. Hammer,Aggregation inequalities in integer programming, Annals Discrete Math. 1 (1977) 145–162.

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  3. F. Harary,Graph theory, Addison-Wesley, Reading (1969).

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  4. P. Manca,On a simple characterization of threshold graphs, Rivista di Matematica per le Scienze Economiche e Sociali, 2 (1979) 3–8.

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, USA

    Frank Harary

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  1. Frank Harary
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Harary, F. The structure of threshold graphs. Rivista di Matematica per le Scienze Economiche e Sociali 2, 169–172 (1979). https://doi.org/10.1007/BF02620304

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  • DOI: https://doi.org/10.1007/BF02620304

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