Trees with a unique maximum independent set and their linear properties

Authors

  • Daniel A. Jaume Departamento de Matem´aticas, Facultad de Ciencias F´ısico-Matem´aticas y Naturales, Universidad Nacional de San Luis, and Instituto de Matem´aticas Aplicadas de San Luis, IMASL-CONICET, San Luis, Argentina
  • Gonzalo Molina Departamento de Matem´aticas, Facultad de Ciencias F´ısico-Matem´aticas y Naturales, Universidad Nacional de San Luis, San Luis, Argentina
  • Rodrigo Sota Departamento de Matem´aticas, Facultad de Ciencias F´ısico-Matem´aticas y Naturales, Universidad Nacional de San Luis, San Luis, Argentina

DOI:

https://doi.org/10.33044/revuma.1145

Abstract

Trees with a unique maximum independent set encode the maxi-mum matching structure in every tree. In this work we study some of their linear properties and give two graph operations, stellare and S-coalescence, which allow building all trees with a unique maximum independent set. The null space structure of any tree can be understood in terms of these graph operations.

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Published

2022-06-08

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