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Enumerating Simple Paths from Connected Induced Subgraphs

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Abstract

We present an exact formula for enumerating the simple paths between any two vertices of a graph. Our formula involves the adjacency matrices of the connected induced subgraphs and remains valid on weighted and directed graphs. As a particular case, we obtain a relation linking the Hamiltonian paths and cycles of a graph to its dominating connected sets.

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Acknowledgements

P.-L. Giscard is grateful for the financial support from the Royal Commission for the Exhibition of 1851. The authors are grateful to an anonymous referee for its many constructive remarks that helped improve the paper.

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Authors and Affiliations

  1. Department of Computer Sciences, University of York, York, UK

    Pierre-Louis Giscard

  2. Laboratoire de Mathématiques Jean Leray, Université de Nantes, Nantes, France

    Paul Rochet

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  1. Pierre-Louis Giscard
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  2. Paul Rochet
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Correspondence to Paul Rochet.

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Giscard, PL., Rochet, P. Enumerating Simple Paths from Connected Induced Subgraphs. Graphs and Combinatorics 34, 1197–1202 (2018). https://doi.org/10.1007/s00373-018-1966-9

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  • DOI: https://doi.org/10.1007/s00373-018-1966-9

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