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On harmonious chromatic number of triple star graph | ||
| Journal of Hyperstructures | ||
| دوره 5، شماره 1، شهریور 2016، صفحه 26-32 اصل مقاله (168.75 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2016.2651 | ||
| نویسنده | ||
| Akhlak Mansuri* | ||
| Department of Mathematics, Lakshmi Narain College Of Technology (LNCT, Bhopal), Kalchuri Nagar, Raisen Road, Bhopal-462021, India | ||
| چکیده | ||
| A Harmonious coloring of a graph G is a proper vertex coloring of G, in which every pair of colors appears on at most one pair of adjacent vertices and the harmonious chromatic number of graph G is the minimum number of colors needed for the harmonious coloring of G and it is denoted byXH(G).The purpose of this paper is to extend the double star graph [12] and to discuss harmonious coloring for central graph, middle graph and total graph of extended double star graph i.e. triple star graph. | ||
| کلیدواژهها | ||
| Central graph؛ Middle graph؛ Total graph؛ Harmonious coloring and Harmonious chromatic number | ||
| مراجع | ||
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[1] J. A. Bondy and U.S.R. Murty, Graph theory with Applications, London, MacMil-lan 1976, 411–467. [2] R. S. Chandel, Vijay Gupta and Akhlak Mansuri, On Harmonious Coloring of Centipede graph Families, Jnanabha, Vol. 42 (2012), pp. 149-154. [3] Keith Edwards, A Bibliography of Harmonious Colourings and Achromatic Num-ber, http://www.computing.dundee.ac.uk/sta/kedwards/biblio.html,2009. [4] Frank Harary, Graph Theory, Narosa Publishing home 1969. [5] F.Harary and S.T.Hedetniemi, The achromatic number of a graph, Journal of Combinatorial Theory 8(1970), 154-161. [6] F. Harary and M. J. Plantholt, On Harmonious Graph Coloring, Utilitas Math-ematica, 23 (1983), pp. 201-207. [7] Vernold Vivin.J, Ph.D Thesis, Harmonious coloring of total graphs, nleaf, central graphs and circumdetic graphs, Bharathiar University, (2007), Coimbatore, India. [8] M. Kubale, Harmonious coloring of graphs, Contemporary Mathematics, 352, American Math. Society, Providence, R.I. (2004), pp. 95-104. [9] Akhlak Mansuri, R . S. Chandel and Vijay Gupta, On Harmonious coloring of M(Ln)and C(Ln), World Applied Programming, Vol 2 , No 3 , March 2012.146-149 [10] Akhlak Mansuri and R. S. Chandel, Harmonious Coloring of Middle Graph of Graphs, Varahmihir J. Math. Sci., Vol. 12 No. 1 (2012), pp. 101-105. [11] Vernold Vivin, M. Venkatachalam and M. M. Akbar Ali, Achromatic coloring on double star graph families, InternationalJournal of Mathematical Combinatorics,3 (2009), 7181. [12] M. Venkatachalam, J. Vernold Vivin and K. Kaliraj, Harmonious Coloring On double star Graph Families, Tamkang Journal of Mathematics, Volume 43, Number 2, 153-158, Summer 2012. [13] V. J. Vernold - M. Venkatachalam - M. M. Akbar Ali, A Note on Achromatic Coloring of Star Graph Families, Filomat 23 (3) (2009), 251255. | ||
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