## Abstract

This paper investigates relationship between algebraic expressions and graphs. Our intent is to simplify graph expressions and eventually find their shortest representations. We prove the monotonicity results allowing to assert that the length of a shortest expression of any subgraph of a given graph is not greater than the length of a shortest expression of the graph. We describe the decomposition method for generating expressions of complete st-dags (two-terminal directed acyclic graphs) and estimate the corresponding expression complexities. Using these findings, we present an 2^{Olog2n} upper bound for the length of a shortest expression for every n-vertex st-dag.

Original language | English |
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Pages (from-to) | 583-594 |

Number of pages | 12 |

Journal | Discrete Applied Mathematics |

Volume | 319 |

DOIs | |

State | Published - 15 Oct 2022 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2022 Elsevier B.V.

## Keywords

- Algebraic expression
- Complexity
- Decomposition
- Edge-labeled graph
- Series–parallel graph
- Two-terminal directed acyclic graph