### Abstract

Let P = [V_{1}, V_{2}, V_{3}, . . ., V_{k}] be a partition of vertex set V (G) of order k ≥ 2. For all V_{i} and V_{j} in P, i ≠ j, remove the edges between V_{i} and V_{j} in graph G and add the edges between V_{i} and V_{j} which are not in G. The graph G_{k} ^{P} thus obtained is called the k-complement of graph G with respect to a partition P. For each set V_{r} in P, remove the edges of graph G inside V_{r} and add the edges of G (the complement of G) joining the vertices of V_{r}. The graph G_{k(i)} ^{P} thus obtained is called the k(i)-complement of graph G with respect to a partition P. In this paper, we study Laplacian energy of generalized complements of some families of graph. An effort is made to throw some light on showing variation in Laplacian energy due to changes in a partition of the graph.

Original language | English |
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Pages (from-to) | 299-315 |

Number of pages | 17 |

Journal | Kragujevac Journal of Mathematics |

Volume | 42 |

Issue number | 2 |

Publication status | Published - 01-01-2018 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Kragujevac Journal of Mathematics*,

*42*(2), 299-315.