Color laplacian energy of generalised complements of a graph

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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}Pk 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}Pk(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).

Original languageEnglish
Pages (from-to)1502-1510
Number of pages9
JournalEngineering Letters
Issue number4
Publication statusPublished - 2021

All Science Journal Classification (ASJC) codes

  • Engineering(all)


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