Color Energy Of A Unitary Cayley Graph

Chandrashekar Adiga; E. Sampathkumar; M.A. Sriraj

Discussiones Mathematicae Graph Theory (2014)

  • Volume: 34, Issue: 4, page 707-721
  • ISSN: 2083-5892

Abstract

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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.

How to cite

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Chandrashekar Adiga, E. Sampathkumar, and M.A. Sriraj. "Color Energy Of A Unitary Cayley Graph." Discussiones Mathematicae Graph Theory 34.4 (2014): 707-721. <http://eudml.org/doc/269826>.

@article{ChandrashekarAdiga2014,
abstract = {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.},
author = {Chandrashekar Adiga, E. Sampathkumar, M.A. Sriraj},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {coloring of a graph; unitary Cayley graph; gcd-graph; color eigenvalues; color energy.; color energy},
language = {eng},
number = {4},
pages = {707-721},
title = {Color Energy Of A Unitary Cayley Graph},
url = {http://eudml.org/doc/269826},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Chandrashekar Adiga
AU - E. Sampathkumar
AU - M.A. Sriraj
TI - Color Energy Of A Unitary Cayley Graph
JO - Discussiones Mathematicae Graph Theory
PY - 2014
VL - 34
IS - 4
SP - 707
EP - 721
AB - 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.
LA - eng
KW - coloring of a graph; unitary Cayley graph; gcd-graph; color eigenvalues; color energy.; color energy
UR - http://eudml.org/doc/269826
ER -

References

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  1. [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. Zbl1306.05140
  2. [2] N. Biggs, Algebraic Graph Theory, Second Edition (Cambridge Mathematical Library, Cambridge University Press, 1993). Zbl0284.05101
  3. [3] C. Godsil and G. Royle, Algebraic Graph Theory (Graduate Texts in Mathematics, Springer, 207, 2001). Zbl0968.05002
  4. [4] I. Gutman, The energy of a graph, Ber. Math. Stat. Sekt. Forschungsz. Graz 103 (1978) 1-22. 
  5. [5] G.H. Hardy and E. M. Wright, An Introdution to Theory of Numbers, Fifth Ed. (Oxford University Press New York, 1980). 
  6. [6] W. Klotz and T. Sander, Some properties of unitary Cayley graphs, Electron. J. Combin. 14 (2007) #R45. Zbl1121.05059
  7. [7] A. Ilić, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881-1889. doi:10.1016/j.laa.2009.06.025 Zbl1175.05086
  8. [8] M. Mollahajiaghaei, The eigenvalues and energy of integral circulant graphs, Trans. Combin. 1 (2012) 47-56. Zbl1272.05115
  9. [9] E. Sampathkumar and M.A. Sriraj, Vertex labeled/colored graphs, matrices and signed graphs, J. Combin. Inform. System Sci., to appear. Zbl1302.05162
  10. [10] W. So, Integral circulant graphs, Discrete Math. 306 (2006) 153-158. doi:10.1016/j.disc.2005.11.006 Zbl1084.05045

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