#
Efficient Algorithm for Generating Maximal L-Reflexive Trees^{ †}

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

**Theorem**

**1.**

**Lemma**

**1.**

**Proof.**

**Lemma**

**2.**

**Proof.**

## 3. Algorithm

**Lemma**

**3.**

**Lemma**

**4.**

**Lemma**

**5.**

**Proof.**

**Lemma**

**6.**

**Proof.**

`mlrt`given in Figure 5. Therefore, the following theorem is straightforward.

**Theorem**

**2.**

`mlrt`$(1,{k}_{1},{k}_{1}/3)$for fixed ${k}_{1}\le d=\mathrm{deg}\left(v\right)$ and $R=6,3,2{\textstyle \frac{2}{5}},2{\textstyle \frac{1}{7}},2,\dots $ correctly generates all maximal L-reflexive trees from Figure 2.

## 4. Experiments

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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$R=6$ | $d=18$: ${N}_{\mathrm{fin}}=1,{N}_{\mathrm{inf}}=0$ |

$d=17$: ${N}_{\mathrm{fin}}=10,{N}_{\mathrm{inf}}=2$ | |

$d=16$: ${N}_{\mathrm{fin}}=6474,{N}_{\mathrm{inf}}=131$ | |

$d=15$: ${N}_{\mathrm{fin}}\ge 20310,{N}_{\mathrm{inf}}\ge 401$ | |

$d=14$: ${N}_{\mathrm{fin}}\ge 13502,{N}_{\mathrm{inf}}\ge 254$ | |

$d=13$: ${N}_{\mathrm{fin}}\ge 24957,{N}_{\mathrm{inf}}\ge 554$ | |

$d=12$: ${N}_{\mathrm{fin}}=0,{N}_{\mathrm{inf}}=1$ | |

$R=3$ | $d=8$: ${N}_{\mathrm{fin}}=10,{N}_{\mathrm{inf}}=2$ |

$d=7$: ${N}_{\mathrm{fin}}=6463,{N}_{\mathrm{inf}}=130$ | |

$d=6$: ${N}_{\mathrm{fin}}=0,{N}_{\mathrm{inf}}=1$ | |

$R=2{\textstyle \frac{2}{5}}$ | $d=7$: ${N}_{\mathrm{fin}}=1,{N}_{\mathrm{inf}}=0$ |

$d=6$: ${N}_{\mathrm{fin}}=32,{N}_{\mathrm{inf}}=4$ | |

$d=5$: ${N}_{\mathrm{fin}}\ge 28498,{N}_{\mathrm{inf}}\ge 298$ | |

$d=4$: ${N}_{\mathrm{fin}}=0,{N}_{\mathrm{inf}}=1$ | |

$R=2{\textstyle \frac{1}{7}}$ | $d=6$: ${N}_{\mathrm{fin}}=2,{N}_{\mathrm{inf}}=0$ |

$d=5$: ${N}_{\mathrm{fin}}=590,{N}_{\mathrm{inf}}=17$ | |

$d=4$: ${N}_{\mathrm{fin}}=0,{N}_{\mathrm{inf}}=1$ | |

$R=2$ | $d=6$: ${N}_{\mathrm{fin}}=1,{N}_{\mathrm{inf}}=0$ |

$d=5$: ${N}_{\mathrm{fin}}=10,{N}_{\mathrm{inf}}=2$ | |

$d=4$: ${N}_{\mathrm{fin}}=0,{N}_{\mathrm{inf}}=1$ |

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**MDPI and ACS Style**

Anđelić, M.; Živković, D.
Efficient Algorithm for Generating Maximal L-Reflexive Trees. *Symmetry* **2020**, *12*, 809.
https://doi.org/10.3390/sym12050809

**AMA Style**

Anđelić M, Živković D.
Efficient Algorithm for Generating Maximal L-Reflexive Trees. *Symmetry*. 2020; 12(5):809.
https://doi.org/10.3390/sym12050809

**Chicago/Turabian Style**

Anđelić, Milica, and Dejan Živković.
2020. "Efficient Algorithm for Generating Maximal L-Reflexive Trees" *Symmetry* 12, no. 5: 809.
https://doi.org/10.3390/sym12050809