Research Article
Randic Color Energy of a Graph
|
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
|
| Volume 171 - Issue 1 |
| Published: Aug 2017 |
| Authors: P. Rajendra |
10.5120/ijca2017914955
|
P. Rajendra . Randic Color Energy of a Graph. International Journal of Computer Applications. 171, 1 (Aug 2017), 1-5. DOI=10.5120/ijca2017914955
@article{ 10.5120/ijca2017914955,
author = { P. Rajendra },
title = { Randic Color Energy of a Graph },
journal = { International Journal of Computer Applications },
year = { 2017 },
volume = { 171 },
number = { 1 },
pages = { 1-5 },
doi = { 10.5120/ijca2017914955 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2017
%A P. Rajendra
%T Randic Color Energy of a Graph%T
%J International Journal of Computer Applications
%V 171
%N 1
%P 1-5
%R 10.5120/ijca2017914955
%I Foundation of Computer Science (FCS), NY, 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
- C. Adiga, E. Sampathkumar and M. A. Sriraj, Color Energy of a Graph, Proc. Jangjeon Math. Soc., 16 (3), (2013), 335-351.
- C. Adiga, E. Sampathkumar and M. A. Sriraj, Color Energy of a Unitary Cayley Graph, Discussiones Mathematicae Graph Theory, 34 (2014), 707-721.
- Bolian Liu, Yufei Huang and Jingfang Feng, A Note on the Randic Spectral Radius, MATCH Commun. Math. Comput. Chem., 68 (2012), 913-916.
- S¸ . Burcu Bozkurt, A. Dilek Gungor and Ivan Gutman, Randic Spectral Radius and Randic Energy, MATCH Commun. Math. Comput. Chem., 64 (2010), 321-334.
- 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.
- D. M. Cvetkovic, M. Doob and H. Sachs, Spectra of Graphs, Theory and Application, Academic Press, New York, USA(1980).
- K. C. Das and S. Sorgun: On Randic Energy of Graphs, MATCH Commun. Math. Comput. Chem., 72 (2014), 227- 238.
- A. Dilek Maden, New Bounds on the Incidence Energy, Randic Energy and Randic Estrada Index, MATCH Commun. Math. Comput. Chem., 74, (2015), 367-387.
- B. Furtula and I. Gutman, Comparing energy and Randic energy, Macedonian Journal of Chemistry and Chemical Engineering, 32(1), (2013), 117-123.
- M. Randic, On Characterization of Molecular Branching, J. Am. Chem. Soc., 97 (1975), 6609-6615.
- V. S. Shigehalli and Kenchappa S. Betageri, Color Laplacian Energy of Graphs, Journal of Computer and Mathematical Sciences, Vol.6(9), 2015, 485-494.
- M.A.Sriraj, Bounds for the Largest Color Eigenvalue and the Color Energy, International J.Math. Combin., Vol.1, (2017), 127-134.
- M. A. Sriraj, Some Studies on Energy of Graphs, Ph. D. Thesis, University of Mysore, Mysore, India, 2014.
- Xueliang Li, Yongtang Shi and I. Gutman, Graph Energy, Springer New York, 2012.
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