## Abstract

Let G_{n} = (V_{n}, E_{n}) be the random subgraph of the n‐cube graph Q^{n} produced as follows: V_{n} is randomly sampled from the vertex set of Q^{n} so that E{x ∈V_{n}} = p_{v} independently for each vertex x ∈Q^{n}. Then E_{n} is randomly sampled from the set of edges induced by V_{n} in Q^{n} so that P{(x, y) ∈ E_{n}} = p_{e} independently for each induced edge (x, y). Let P_{v} and p_{e} be fixed probabilities such that 0 < p = p_{v}p_{e} ⩽ 1 and m_{p} = [−1 /log_{2}(1 − p)]. We show that for the radius R(G_{n}) and the diameter D(G_{n}) of the main component of G_{n} almost surely the following inequalities hold (Formula Presented.) . © 1993 John Wiley & Sons, Inc.

Original language | English (US) |
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Pages (from-to) | 215-229 |

Number of pages | 15 |

Journal | Random Structures & Algorithms |

Volume | 4 |

Issue number | 2 |

DOIs | |

State | Published - 1993 |

Externally published | Yes |

## ASJC Scopus subject areas

- Software
- Mathematics(all)
- Computer Graphics and Computer-Aided Design
- Applied Mathematics