Grundy Number of Some Chordal Graphs
DOI:
https://doi.org/10.14419/ijet.v7i4.10.20708Published:
2018-10-02Keywords:
Grundy coloring, Grundy number, Ladder graph, Tadpole graph, wheel graph, Fan graph, Double fan graph.Abstract
For a given graph G and integer k, the Coloring problem is that of testing whether G has a k-coloring, that is, whether there exists a vertex mapping c : V → {1, 2, . . .} such that c(u) 12≠"> c(v) for every edge uv ∈ E. For proper coloring, colors assigned must be minimum, but for Grundy coloring which should be maximum. In this instance, Grundy numbers of chordal graphs like Cartesian product of two path graphs, join of the path and complete graphs and the line graph of tadpole have been executed
References
[1] Alkhateeb, On b-colorings and b-continuity of graphs, Ph.D. Thesis, Technische Univer-sittBergakademie, Freiberg, Germany, 2012.
[2] R. Balakrishnan and K. Ranganathan A textbook of Graph Theory, Springer, New York, 2012.
[3] Brice Effantin.et.al,Grundy number of graphs, Discussiones Mathematicae Graph Theory 27 (2007 ) 5-18.
[4] Chandrakumar.s,Nicholas.T,b-coloring in square of Cartesian product of two cy-cles,Anals of pure and Applied Mathematics, Vol. 1, No. 2, 2012, 131-137, ISSN: 2279-087X (P), 2279-0888(online),Nov 2012.
[5] Cvetkocic, D. M, Doob, M. and Sachs, H, Spectra of graphs - Theory and Applica-tion,Acadamicpress,New york,1980.
[6] Douglas B.west,Introduction to Graph Theory,Prentice-Hall of India private Lim-ited,NewDelhi,1999.
[7] Francis Raj S. and BalakrishnanR.,Bounds for the b-chromatic number of Cartesianproduct of some families of graphs, to appear in Ars Combinatoria.
[8] F. Harary, Graph theory, Addison-Wesley publishing Company, Massachusetts, 1970
[9] F. Havet, M. Aste, C. Linhares Sales. Grundy number and products of graphs. DiscreteMathematics. 310:14821490, 2010.
[10] Irving R. W. and Man love D. F., The b-chromatic number of a graph, Dis-crete.Appl.Math.91 (1991) pp. 127-141.
[11] T.R.Jensen,B.Toft,Graph Coloring problems,Wiley,New York,1995.
[12] Kouider and Zaker, The bounds for the b-chromatic number for various graphs, Discrete Mathematics 306 (2006) 617 623.
[13] Purna Chandra Biswal,Discrete Mathematics and Graph theory, Eastern Economy Edi- tion,PHI Learning Private Ltd.,Delhi(2015),Page 275.
[14] Tau_k Faik.et.al,On the b-continuity property of graphs, Discrete Applied Mathemat-ics,volume 155,Issue 13,Page 1761-68,2007
[15] Mrs. D. Vijayalakshmi and Dr. K. Thilagavathi, b-coloring inthe context of some graphoperations, International Journal of Mathematical Archive, 3(4) (2012), 1439-1442.
[16] M. Zaker. Results on the Grundy chromatic number of graphs. Discrete Mathematics, 306 (2006) 3166-3173.
[17] C. Germain and H. Kheddouci, Grundy coloring of powers of graphs, to appearin Discrete Math. 2006.
[18] C. Parks and J. Rhyne, Grundy Coloring for Chessboard Graphs, SeventhNorth Carolina Mini-Conference on Graph Theory, Combinatorics, and Computing (2002).
[19] Victor Campos. et. al, New bounds on the Grundy number of products of graphs, HAL, ISSN 0249-6399, April 2010.
[20] Linfan Mao,Mathematical Combinatorics, Vol. 2/2012: international book series,Page 61.
[21] S.P.Hande.et.al ,Zegreb indices on some graph operations of Tadpole graph,Inernational journal of Computers andMathematicl Sciences,ISSN 2347-8527,Volume 3,Issue 9,November 2014.
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Accepted 2018-10-01
Published 2018-10-02