## Abstract

Let n > m ≥ 3 be integers. The framing number fr(C_{m}, C_{n}) of a cycle C_{m} of length m and a cycle C_{n} of length n is defined as the minimum order of a graph every vertex of which belongs to an induced C_{m} and an induced C_{n}. The framing number fr ( C_{m}, C_{n}) of a directed cycle C_{m} of length m and a directed cycle C_{n} of length n is defined as the minimum order of a digraph every vertex of which belongs to an induced C_{m} and an induced C_{n}. In this paper we determine all the nonisomorphic frames of those pairs of cycles C_{m} and C_{n} which have framing number n + 2. Thereafter we characterize all those pairs of directed cycles C_{m} and C_{n} which have framing number n + 2 and, for each such pair (m, n), we determine all the nonisomorphic frames of C_{m} and C_{n}.

Original language | English |
---|---|

Pages (from-to) | 647-660 |

Number of pages | 14 |

Journal | Indian Journal of Pure and Applied Mathematics |

Volume | 28 |

Issue number | 5 |

Publication status | Published - May 1997 |

Externally published | Yes |

## ASJC Scopus subject areas

- General Mathematics
- Applied Mathematics