### Abstract

If G is a graph such that the deletion from G of the points in each closed neighborhood results in the complete graph K_{n}, then we say that G is K_{n}-residual. Similarly, if the removal of m consecutive closed neighborhoods yields K_{n}, then G is called m-K_{n} -residual. We determine the minimum order of the m-K_{n}-residual graphs for all m and n. The minimum order of the connected K_{n}-residual graphs is found and all the extremal graphs are specified.

Original language | English |
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Pages (from-to) | 117-123 |

Number of pages | 7 |

Journal | Annals of Discrete Mathematics |

Volume | 6 |

Issue number | C |

DOIs | |

Publication status | Published - 1980 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

### Cite this

*Annals of Discrete Mathematics*,

*6*(C), 117-123. https://doi.org/10.1016/S0167-5060(08)70698-8

**Residually-Complete Graphs.** / Erdős, P.; Harary, Frank; Klawe, Maria.

Research output: Contribution to journal › Article

*Annals of Discrete Mathematics*, vol. 6, no. C, pp. 117-123. https://doi.org/10.1016/S0167-5060(08)70698-8

}

TY - JOUR

T1 - Residually-Complete Graphs

AU - Erdős, P.

AU - Harary, Frank

AU - Klawe, Maria

PY - 1980

Y1 - 1980

N2 - If G is a graph such that the deletion from G of the points in each closed neighborhood results in the complete graph Kn, then we say that G is Kn-residual. Similarly, if the removal of m consecutive closed neighborhoods yields Kn, then G is called m-Kn -residual. We determine the minimum order of the m-Kn-residual graphs for all m and n. The minimum order of the connected Kn-residual graphs is found and all the extremal graphs are specified.

AB - If G is a graph such that the deletion from G of the points in each closed neighborhood results in the complete graph Kn, then we say that G is Kn-residual. Similarly, if the removal of m consecutive closed neighborhoods yields Kn, then G is called m-Kn -residual. We determine the minimum order of the m-Kn-residual graphs for all m and n. The minimum order of the connected Kn-residual graphs is found and all the extremal graphs are specified.

UR - http://www.scopus.com/inward/record.url?scp=77957035445&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957035445&partnerID=8YFLogxK

U2 - 10.1016/S0167-5060(08)70698-8

DO - 10.1016/S0167-5060(08)70698-8

M3 - Article

VL - 6

SP - 117

EP - 123

JO - Annals of Discrete Mathematics

JF - Annals of Discrete Mathematics

SN - 0167-5060

IS - C

ER -