### Abstract

A set of vertices of a graph whose removal leaves an acyclic graph is called a decycling set of the graph. The minimum size of a decycling set of a graph G is referred to as the decycling number of G, denoted by δ(G). In this paper, we study the decycling number of the Cartesian product of two paths, δ(P_{m}-P_{n}), and obtain several new results. Mainly, we prove that ⌈(m-1)(n-1)+13⌉≤ (P_{m} □ P_{n}≤ (m-1)(n-1)+13 +1. Moreover, we obtain the exact value of δ(P_{m}P_{n}) for some classes (modulo 6) of pairs (m, n).

Original language | English |
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Article number | 1450033 |

Journal | Discrete Mathematics, Algorithms and Applications |

Volume | 6 |

Issue number | 3 |

DOIs | |

State | Published - 1 Sep 2014 |

### Keywords

- Decycling number
- feedback vertex number
- grids

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## Cite this

Lien, M. Y., Fu, H. L., & Shih, C. H. (2014). The decycling number of P

_{m}□ P_{n}∗.*Discrete Mathematics, Algorithms and Applications*,*6*(3), [1450033]. https://doi.org/10.1142/S1793830914500335