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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

Permanents and Determinants of Graphs: A Cycle Polynomial Approach

Edward J. Farrell 1, John W. Kennedy2, Louis V. Quintas 2
1Centre for Graph Polymomials Department of Mathematics University of the West Indies St. Augustine, Trinidad
2 Department of Mathematics Pace University New York, NY 10038, USA
  • Published: 28/02/2000

Abstract

Various connections have been established between the permanent and the determinant of the adjacency matrix of a graph. Connections are also made between these scalars and the number of perfect matchings in a graph. We establish conditions for graphs to have determinant 0 or \(\pm1\). Necessary conditions and sufficient conditions are obtained for graphs to have permanent equal to 0 or to 1.

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Citation
Edward J. Farrell , John W. Kennedy, Louis V. Quintas . Permanents and Determinants of Graphs: A Cycle Polynomial Approach[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 032. 129-138. DOI: .