## Abstract

The color energy of a graph is defined as sum of absolute color eigenvalues of graph, denoted by E_{c}(G). Let G_{c} = (V, E) be a color graph and P = {V_{1}, V_{2}, …, V_{k} } be a partition of V of order k ≥ 1. The k-color complement {G_{c}}^{P}k of G_{c} 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 the edges which are not in G_{c} such that end vertices have different colors. For each set V_{r} in the partition P, remove the edges of G_{c} inside V_{r}, and add the edges of G_{c} (the complement of G_{c}) joining the vertices of V_{r}. The graph {G_{c}}^{P}_{k(i)} thus obtained is called the k(i)− color complement of G_{c} 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).

Original language | English |
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Pages (from-to) | 1502-1510 |

Number of pages | 9 |

Journal | Engineering Letters |

Volume | 29 |

Issue number | 4 |

Publication status | Published - 2021 |

## All Science Journal Classification (ASJC) codes

- Engineering(all)