## Abstract

Let P = {V_{1},V_{2}, · · ·,V_{k} } be a partition of vertex set V of G. The k−complement of G denoted by G^{P}k^{is} defined as follows: for all V_{i} and V_{j} in P, i ≠ j, remove the edges between V_{i} and V_{j} and add edges between V_{i} and V_{j} which are not in G. The graph G is k-self complementary with respect to P if G^{P}^{∼}k = G. The k(i)-complement G^{P}k(i)of a graph G with respect to P is defined as follows: for all Vr ∈ P, remove edges inside V_{r} and add edges which are not in V_{r}. In this paper we provide sufficient conditions for G^{P}k and G^{P}k(i) to be disconnected, regular, line preserving and Eulerian.

Original language | English |
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Pages (from-to) | 2917-2925 |

Number of pages | 9 |

Journal | Journal of Mathematical and Computational Science |

Volume | 10 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2020 |

## All Science Journal Classification (ASJC) codes

- General Mathematics
- Computational Theory and Mathematics