### Abstract

Let G be a finite simple graph on n vertices. 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^{P}k thus obtained is called the k−complement of graph G with respect to the partition P. Let P = {V_{1}, V_{2}, V_{3}, …, V_{k}} be a partition of vertex set V (G) of order k ≥ 1. 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 (formula presented) thus obtained is called the k(i)−complement of graph G with respect to the partition P. Energy of a graph G is the sum of absolute eigenvalues of G. In this paper, we study energy of generalized complements of some families of graph. An effort is made to throw some light on showing variation in energy due to changes in the partition of the graph.

Original language | English |
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Pages (from-to) | 131-136 |

Number of pages | 6 |

Journal | Engineering Letters |

Volume | 28 |

Issue number | 1 |

Publication status | Published - 01-01-2020 |

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### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

*Engineering Letters*,

*28*(1), 131-136.