On Acyclic Coloring of Mycielskians

Authors

  • Kaliraj K. Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600005, Tamil Nadu
  • Kowsalya V. Research & Development Centre, Bharathiar University, Coimbatore 641046, Tamil Nadu
  • Vernold Vivin J. Department of Mathematics, University College of Engineering Nagercoil (Anna University Constituent College), Konam, Nagercoil 629004, Tamilnadu

DOI:

https://doi.org/10.26713/jims.v9i3.949

Keywords:

Acyclic coloring, Mycielskian

Abstract

An acyclic coloring of a graph \(G\) is a proper vertex coloring such that the induced subgraph of any two color classes is acyclic. The minimum number of colors needed to acyclically color the vertices of a graph \(G\) is called as acyclic chromatic number and is denoted by \(\chi_a(G)\). In this paper, we give the exact value of the acyclic chromatic number of Mycielskian graph of cycles, paths, complete graphs and complete bipartite graphs.

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References

J.A.Bondy and U.S.R.Murty, Graph theory with Applications, London, MacMillan (1976).

G.J. Chang, L. Huang and X. Zhu, Circular chromatic numbers of Mycielski's graphs, Discrete Math. 205(1–3) (1999), 23 – 37.

B. Grünbaum, Acyclic colorings of planar graphs, Israel J. Math. 14 (1973), 390 – 408.

F. Harary, Graph Theory, Narosa Publishing House, New Delhi (1969).

J. Miškuf, R. Å krekovski and M. Tancer, Backbone colorings and generalized Mycielski graphs, SIAM J. Discrete Math. 23(2) (2009), 1063 – 1070.

J. Mycielski, Sur le coloriage des graphes, Colloq. Math. 3 (1955), 161 – 162.

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Published

2017-10-30
CITATION

How to Cite

K., K., V., K., & J., V. V. (2017). On Acyclic Coloring of Mycielskians. Journal of Informatics and Mathematical Sciences, 9(3), 835–842. https://doi.org/10.26713/jims.v9i3.949

Issue

Vol. 9 No. 3 (2017)

Section

Research Articles

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