Color energy of a unitary Cayley graph

The Total π-Electron Energy Saga

“…In reality, the number of existing graph energies may be still greater, and more such will for sure appear in the future. 1) (ordinary) graph energy [12] 2) extended adjacency energy [30] 3) Laplacian energy [36] 4) energy of matrix [41] 5) minimum robust domination energy [49] 6) energy of set of vertices [50] 7) distance energy [37] 8) Laplacian-energy-like invariant [51] 9) Consonni-Todeschini energies [40] 10) energy of (0,1)-matrix [52] 11) incidence energy [53] 12) maximum-degree energy [54] 13) skew Laplacian energy [55] 14) oriented incidence energy [56] 15) skew energy [57] 16) Randić energy [39] 17) normalized Laplacian energy [38] 18) energy of matroid [58] 19) energy of polynomial [42] 20) Harary energy [59] 21) sum-connectivity energy [60] 22) second-stage energy [61] 23) signless Laplacian energy [62] 24) PI energy [63] 25) Szeged energy [64] 26) He energy [65] 27) energy of orthogonal matrix [66] 28) common-neighborhood energy [67] 29) matching energy [43] 30) Seidel energy [68] 31) ultimate energy [69] 32) minimum-covering energy [70] 33) resistance-distance energy [71] 34) Kirchhoff energy [72] 35) color energy [73] 36) normalized incidence energy [74] 37) Laplacian distance energy [75] 38) Laplacian incidence energy [76] 39) Laplacian minimum dominating energy …”

Randic Color Energy of a Graph

“…Motivated by Color Energy of a Graph [1] and Randić Matrix and Randić Energy [5], have obtained a new matrix called Randić color matrix. Let G be a simple colored graph with n vertices.…”

“…A coloring of graph [1] G is a coloring of its vertices such that no two adjacent vertices receive the same color. The minimum number of colors needed for coloring of a graph G is called …”

Further results on color energy of graphs

“…Recently Adiga et al [1] introduced the concept of color energy of a graph based on the color matrix of the graph. If the eigenvalues of A c (G) are λ 1 , λ 2 , .…”

“…Given a colored graph G, its color energy E 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 Adiga et al [1]. In this article, we obtain some new bounds for the color energy of graphs and establish relationship between color energy E c (G) and energy 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.…”