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Randic Color Energy of a Graph

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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2017
Authors:
P. Rajendra
10.5120/ijca2017914955

P Rajendra. Randic Color Energy of a Graph. International Journal of Computer Applications 171(1):1-5, August 2017. BibTeX

@article{10.5120/ijca2017914955,
	author = {P. Rajendra},
	title = {Randic Color Energy of a Graph},
	journal = {International Journal of Computer Applications},
	issue_date = {August 2017},
	volume = {171},
	number = {1},
	month = {Aug},
	year = {2017},
	issn = {0975-8887},
	pages = {1-5},
	numpages = {5},
	url = {http://www.ijcaonline.org/archives/volume171/number1/28142-2017914955},
	doi = {10.5120/ijca2017914955},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}
}

Abstract

Let G = (V,E) be a colored graph with vertex set V(G) and edge set E(G) with chromatic number (G) and di is the degree of a vertex vi. The Randic matrix R(G) = (rij) of a graph G, is defined by rij = 1⁄√didj , if the vertices vi and vj are adjacent and rij = 0, otherwise. The Randic energy [5] RE(G) is the sum of absolute values of the eigenvalues of R(G). The concept of Randic color energy ERC(G) of a colored graph G is defined and obtained the Randic color energy ERC(G) of some graphs with minimum number of colors.

References

  1. C. Adiga, E. Sampathkumar and M. A. Sriraj, Color Energy of a Graph, Proc. Jangjeon Math. Soc., 16 (3), (2013), 335-351.
  2. C. Adiga, E. Sampathkumar and M. A. Sriraj, Color Energy of a Unitary Cayley Graph, Discussiones Mathematicae Graph Theory, 34 (2014), 707-721.
  3. Bolian Liu, Yufei Huang and Jingfang Feng, A Note on the Randic Spectral Radius, MATCH Commun. Math. Comput. Chem., 68 (2012), 913-916.
  4. S¸ . Burcu Bozkurt, A. Dilek Gungor and Ivan Gutman, Randic Spectral Radius and Randic Energy, MATCH Commun. Math. Comput. Chem., 64 (2010), 321-334.
  5. S¸ . Burcu Bozkurt, A. Dilek Gungor, Ivan Gutman and A. Sinan C¸ evik, Randic Matrix and Randic Energy, MATCH Commun. Math. Comput. Chem., 64 (2010), 239-250.
  6. D. M. Cvetkovic, M. Doob and H. Sachs, Spectra of Graphs, Theory and Application, Academic Press, New York, USA(1980).
  7. K. C. Das and S. Sorgun: On Randic Energy of Graphs, MATCH Commun. Math. Comput. Chem., 72 (2014), 227- 238.
  8. A. Dilek Maden, New Bounds on the Incidence Energy, Randic Energy and Randic Estrada Index, MATCH Commun. Math. Comput. Chem., 74, (2015), 367-387.
  9. B. Furtula and I. Gutman, Comparing energy and Randic energy, Macedonian Journal of Chemistry and Chemical Engineering, 32(1), (2013), 117-123.
  10. M. Randic, On Characterization of Molecular Branching, J. Am. Chem. Soc., 97 (1975), 6609-6615.
  11. V. S. Shigehalli and Kenchappa S. Betageri, Color Laplacian Energy of Graphs, Journal of Computer and Mathematical Sciences, Vol.6(9), 2015, 485-494.
  12. M.A.Sriraj, Bounds for the Largest Color Eigenvalue and the Color Energy, International J.Math. Combin., Vol.1, (2017), 127-134.
  13. M. A. Sriraj, Some Studies on Energy of Graphs, Ph. D. Thesis, University of Mysore, Mysore, India, 2014.
  14. Xueliang Li, Yongtang Shi and I. Gutman, Graph Energy, Springer New York, 2012.

Keywords

Colored graph, Randic matrix, Randic color energy