ON STAR CHROMATIC NUMBER OF PRISM GRAPH FAMILIES

Year 2019, Volume: 9 Issue: 3, 687 - 692, 01.09.2019

Vernold Vıvın J. Kowsalya V. Vımal Kumar S.

Abstract

In this paper, we nd the star chromatic number s for the central graph of prism graph C Yn , line graph of prism graph L Yn , middle graph of prism graph M Yn and the total graph of prism graph T Yn for all n 3.

Keywords

Star coloring, prism graph, central graph, line graph, middle graph and total graph.

References

• Albertson, Michael O., Chappell, Glenn G., Kierstead, Hal A., K¨undgen, Andr´e and Ramamurthi, R., (2004), Coloring with no 2-Colored P4’s, The Electronic Journal of Combinatorics 11, Paper # R26, 13.
• Bondy, J. A, and Murty U. S. R, (1976), Graph theory with Applications, MacMillan, London.
• Branko Gr¨unbaum, (1973), Acyclic colorings of planar graphs, Israel J. Math 14, pp. 390-408.
• Danuta Michalak, (1981), On middle and total graphs with coarseness number equal 1, Springer Verlag Graph Theory, Lagow proceedings, Berlin Heidelberg, New York, Tokyo, pp. 139-150.
• Frank Harary, (1969), Graph Theory, Narosa Publishing home, New Delhi.
• Fertin, Guillaume, Raspaud, Andr´e and Reed, Bruce, (2004), Star coloring of graphs, Journal of Graph Theory 47 (3), pp. 163-182.
• Thomas F.Coleman and Jin-Yi Cai, (1986), The cyclic coloring problem and estimation of sparse Hessian matrices, SIAM J. Alg. Disc. Math 7, pp. 221-235.
• Thomas F.Coleman and Jorge J.Mor´e, (1984), Estimation of sparse Hessian matrices and graph coloring problems, Mathematical Programming, 2 (3), pp. 243-270.
• Vernold Vivin.J, Ph.D Thesis, (2007), Harmonious coloring of total graphs, n-leaf, central graphs and circumdetic graphs, Bharathiar University, Coimbatore, India.