Color Energy Of A Unitary Cayley Graph

• Autorzy: Chandrashekar Adiga , E. Sampathkumar , M.A. Sriraj
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

coloring of a graph; unitary Cayley graph; gcd-graph; color eigenvalues; color energy.

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2014
• Tom: 34
• Numer: 4
• Strony: 707-721

Daty

wydano

2014-11-01

otrzymano

2013-01-31

poprawiono

2013-09-17

zaakceptowano

2013-10-16

online

2014-11-15

Twórcy

autor

Chandrashekar Adiga

• Department of Studies in Mathematics University of Mysore Manasagangotri Mysore – 570 006, India

autor

E. Sampathkumar

• Department of Studies in Mathematics University of Mysore Manasagangotri Mysore – 570 006, India

autor

M.A. Sriraj

• Department of Studies in Mathematics University of Mysore Manasagangotri Mysore – 570 006, India/The first author is thankful to the university grants commission Goverment of India for the financial support under the grant F.510/2/SAP-DRS/2011. The second and third authors are thankful to DST for its financial support under the project SR/S4/MS 236/04

Bibliografia

• [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 Introdution 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

Identyfikatory

DOI

10.7151/dmgt.1767