Nayak, Swathi and D'souza, Sabitha and Bhat, Pradeep G
(2021)
*Color Laplacian Energy of Generalised Complements of a Graph.*
Engineering Letters, 29 (4).
ISSN 1816-093X

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## Abstract

The color energy of a graph is defined as sum of absolute color eigenvalues of graph, denoted by Ec(G). Let Gc = (V, E) be a color graph and P = {V1, V2, . . . , Vk} be a partition of V of order k ≥ 1. The k -color complement {Gc} P k of Gc is defined as follows: For all Vi and Vj in P, i ̸= j, remove the edges between Vi and Vj and add the edges which are not in Gc such that end vertices have different colors. For each set Vr in the partition P, remove the edges of Gc inside Vr, and add the edges of Gc (the complement of Gc ) joining the vertices of Vr. The graph {Gc} P k(i) thus obtained is called the k(i)− color complement of Gc with respect to the partition P of V . In this paper, we compute color Laplacian energy of generalised complements of few standard graphs. Color Laplacian energy depends on assignment of colors to the vertices and the partition of V (G).

Item Type: | Article |
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Uncontrolled Keywords: | —k−color complement, k(i)−color complement, color Laplacian energy, color Laplacian spectrum |

Subjects: | Engineering > MIT Manipal > Mathematics |

Depositing User: | MIT Library |

Date Deposited: | 20 Jan 2022 09:00 |

Last Modified: | 20 Jan 2022 09:00 |

URI: | http://eprints.manipal.edu/id/eprint/158111 |

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