### 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.

}

*Kragujevac Journal of Mathematics*, vol. 42, no. 2, pp. 299-315.

**Laplacian energy of generalized complements of a graph.** / Gowtham, H. J.; D'Souza, Sabitha; Bhat, Pradeep G.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Laplacian energy of generalized complements of a graph

AU - Gowtham, H. J.

AU - D'Souza, Sabitha

AU - Bhat, Pradeep G.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Let P = [V1, V2, V3, . . ., Vk] be a partition of vertex set V (G) of order k ≥ 2. For all Vi and Vj in P, i ≠ j, remove the edges between Vi and Vj in graph G and add the edges between Vi and Vj which are not in G. The graph Gk P thus obtained is called the k-complement of graph G with respect to a partition P. For each set Vr in P, remove the edges of graph G inside Vr and add the edges of G (the complement of G) joining the vertices of Vr. The graph Gk(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.

AB - Let P = [V1, V2, V3, . . ., Vk] be a partition of vertex set V (G) of order k ≥ 2. For all Vi and Vj in P, i ≠ j, remove the edges between Vi and Vj in graph G and add the edges between Vi and Vj which are not in G. The graph Gk P thus obtained is called the k-complement of graph G with respect to a partition P. For each set Vr in P, remove the edges of graph G inside Vr and add the edges of G (the complement of G) joining the vertices of Vr. The graph Gk(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.

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M3 - Article

VL - 42

SP - 299

EP - 315

JO - Kragujevac Journal of Mathematics

JF - Kragujevac Journal of Mathematics

SN - 1450-9628

IS - 2

ER -