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Further results on color energy of graphs. (English) Zbl 1380.05067
Summary: Given a colored graph \(G\), its color energy \(\mathsf{E}_{\mathsf{c}}(G)\) is defined as the sum of the absolute values of the eigenvalues of the color matrix of \(G\). The concept of color energy was introduced by C. Adiga et al. [Proc. Jangjeon Math. Soc. 16, No. 3, 335–351 (2013; Zbl 1306.05140)]. In this article, we obtain some new bounds for the color energy of graphs and establish relationship between color energy \(\mathsf{E}_{\mathsf{c}}(G)\) and energy \(\mathsf{E}(G)\) of a graph \(G\). Further, we construct some new families of graphs in which one is non-co-spectral color-equienergetic with some families of graphs and another is color-hyperenergetic. Also we derive explicit formulas for their color energies.
MSC:
05C15 Coloring of graphs and hypergraphs
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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