Color energy of a unitary Cayley graph
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 4, pp. 707-721.

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Let G be a vertex colored graph. The minimum number χ(G) of colors needed for coloring of a graph G is called the chromatic number. Recently, Adiga et al. [1] have introduced the concept of color energy of a graph Ec(G) and computed the color energy of few families of graphs with χ(G) colors. In this paper we derive explicit formulas for the color energies of the unitary Cayley graph Xn, the complement of the colored unitary Cayley graph (Xn)c and some gcd-graphs.
Keywords: coloring of a graph, unitary Cayley graph, gcd-graph, color eigenvalues, color energy
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Adiga, Chandrashekar; Sampathkumar, E.; Sriraj, M.A. Color energy of a unitary Cayley graph. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 4, pp. 707-721. http://geodesic.mathdoc.fr/item/DMGT_2014_34_4_a4/

[1] C. Adiga, E. Sampathkumar, M.A. Sriraj and A.S. Shrikanth, Color energy of a graph, Proc. Jangjeon Math. Soc. 16 3 (2013) 335-351.

[2] N. Biggs, Algebraic Graph Theory, Second Edition (Cambridge Mathematical Library, Cambridge University Press, 1993).

[3] C. Godsil and G. Royle, Algebraic Graph Theory (Graduate Texts in Mathematics, Springer, 207, 2001).

[4] I. Gutman, The energy of a graph, Ber. Math. Stat. Sekt. Forschungsz. Graz 103 (1978) 1-22.

[5] G.H. Hardy and E. M. Wright, An Introduction to Theory of Numbers, Fifth Ed. (Oxford University Press New York, 1980).

[6] W. Klotz and T. Sander, Some properties of unitary Cayley graphs, Electron. J. Combin. 14 (2007) #R45.

[7] A. Ilić, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881-1889. doi:10.1016/j.laa.2009.06.025

[8] M. Mollahajiaghaei, The eigenvalues and energy of integral circulant graphs, Trans. Combin. 1 (2012) 47-56.

[9] E. Sampathkumar and M.A. Sriraj, Vertex labeled/colored graphs, matrices and signed graphs, J. Combin. Inform. System Sci., to appear.

[10] W. So, Integral circulant graphs, Discrete Math. 306 (2006) 153-158. doi:10.1016/j.disc.2005.11.006