### Abstract

A subset of vertices of a graph is said to be 2-arc closed if it contains every vertex that is adjacent to at least two vertices in the subset. In this paper, 2-arc closed subsets generated by pairs of vertices at distance at most 2 are studied. Several questions are posed about the structure of such subsets and the relationships between two such subsets, and examples are given from the class of partition graphs. (C) 2003 Wiley Periodicals, Inc.

Original language | English |
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Pages (from-to) | 350-364 |

Journal | Journal of Graph Theory |

Volume | 42 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2003 |

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## Cite this

Conder, M., Morton, M., & Praeger, C. (2003). Two-Arc Closed Subsets of Graphs.

*Journal of Graph Theory*,*42*(4), 350-364. https://doi.org/10.1002/jgt.10102