### Abstract

The graph G is called a porcupine, if G{divides}A is a complete graph for some set A, every other vertex has degree one, and its only edge is joined to A. In this paper a conjecture of Bollobás is settled almost completely. Namely, it is proved that if G is a graph on n vertices of diameter 3 with maximum degree D, D > 2.31 {Mathematical expression}, D ≠ (n - 1)/2 and it has the mimimum number of edges, then it is a porcupine.

Original language | English |
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Pages (from-to) | 333-337 |

Number of pages | 5 |

Journal | Graphs and Combinatorics |

Volume | 6 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 1990 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Mathematics(all)

### Cite this

**Graphs of diameter 3 with the minimum number of edges.** / Füredi, Z.

Research output: Contribution to journal › Article

*Graphs and Combinatorics*, vol. 6, no. 4, pp. 333-337. https://doi.org/10.1007/BF01787701

}

TY - JOUR

T1 - Graphs of diameter 3 with the minimum number of edges

AU - Füredi, Z.

PY - 1990/12

Y1 - 1990/12

N2 - The graph G is called a porcupine, if G{divides}A is a complete graph for some set A, every other vertex has degree one, and its only edge is joined to A. In this paper a conjecture of Bollobás is settled almost completely. Namely, it is proved that if G is a graph on n vertices of diameter 3 with maximum degree D, D > 2.31 {Mathematical expression}, D ≠ (n - 1)/2 and it has the mimimum number of edges, then it is a porcupine.

AB - The graph G is called a porcupine, if G{divides}A is a complete graph for some set A, every other vertex has degree one, and its only edge is joined to A. In this paper a conjecture of Bollobás is settled almost completely. Namely, it is proved that if G is a graph on n vertices of diameter 3 with maximum degree D, D > 2.31 {Mathematical expression}, D ≠ (n - 1)/2 and it has the mimimum number of edges, then it is a porcupine.

UR - http://www.scopus.com/inward/record.url?scp=34249963718&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249963718&partnerID=8YFLogxK

U2 - 10.1007/BF01787701

DO - 10.1007/BF01787701

M3 - Article

VL - 6

SP - 333

EP - 337

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

SN - 0911-0119

IS - 4

ER -