On the Total Graph of Mycielski Graphs, Central Graphs and Their Covering Numbers

H.P. Patil; R. Pandiya Raj

Discussiones Mathematicae Graph Theory (2013)

  • Volume: 33, Issue: 2, page 361-371
  • ISSN: 2083-5892

Abstract

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The technique of counting cliques in networks is a natural problem. In this paper, we develop certain results on counting of triangles for the total graph of the Mycielski graph or central graph of star as well as completegraph families. Moreover, we discuss the upper bounds for the number of triangles in the Mycielski and other well known transformations of graphs. Finally, it is shown that the achromatic number and edge-covering number of the transformations mentioned above are equated.

How to cite

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H.P. Patil, and R. Pandiya Raj. "On the Total Graph of Mycielski Graphs, Central Graphs and Their Covering Numbers." Discussiones Mathematicae Graph Theory 33.2 (2013): 361-371. <http://eudml.org/doc/268246>.

@article{H2013,
abstract = {The technique of counting cliques in networks is a natural problem. In this paper, we develop certain results on counting of triangles for the total graph of the Mycielski graph or central graph of star as well as completegraph families. Moreover, we discuss the upper bounds for the number of triangles in the Mycielski and other well known transformations of graphs. Finally, it is shown that the achromatic number and edge-covering number of the transformations mentioned above are equated.},
author = {H.P. Patil, R. Pandiya Raj},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {total graph; central graph; middle graph; Mycielski graph; independence number; covering number; edge independence number; edge covering number; chromatic number; achromatic number},
language = {eng},
number = {2},
pages = {361-371},
title = {On the Total Graph of Mycielski Graphs, Central Graphs and Their Covering Numbers},
url = {http://eudml.org/doc/268246},
volume = {33},
year = {2013},
}

TY - JOUR
AU - H.P. Patil
AU - R. Pandiya Raj
TI - On the Total Graph of Mycielski Graphs, Central Graphs and Their Covering Numbers
JO - Discussiones Mathematicae Graph Theory
PY - 2013
VL - 33
IS - 2
SP - 361
EP - 371
AB - The technique of counting cliques in networks is a natural problem. In this paper, we develop certain results on counting of triangles for the total graph of the Mycielski graph or central graph of star as well as completegraph families. Moreover, we discuss the upper bounds for the number of triangles in the Mycielski and other well known transformations of graphs. Finally, it is shown that the achromatic number and edge-covering number of the transformations mentioned above are equated.
LA - eng
KW - total graph; central graph; middle graph; Mycielski graph; independence number; covering number; edge independence number; edge covering number; chromatic number; achromatic number
UR - http://eudml.org/doc/268246
ER -

References

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  1. [1] F. Harary, Graph Theory (Narosa Publishing Home, 1969). 
  2. [2] G.J. Chang, L. Huang and X. Zhu, Circular chromatic numbers of Mycielski’s graphs, Discrete Math. 205 (1999) 23-37. doi:10.1016/S0012-365X(99)00033-3[WoS][Crossref] 
  3. [3] G. Kortsarz and S. Shende, Approximating the Achromatic Number Problem on Bipartite Graphs, (Springer Berlin / Heidelberg, 2003) LNCS Vol. 2832 385-396.[WoS] Zbl1266.68230
  4. [4] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (London, MacMillan, 1976). Zbl1226.05083
  5. [5] M.M. Ali Akbar, K. Kaliraj and Vernold J. Vivin, On equitable coloring of central graphs and total graphs, Electron. Notes Discrete Math. 33 (2009) 1-6. doi:10.1016/j.endm.2009.03.001[Crossref] Zbl1267.05227
  6. [6] Ramakrishnan, MPhil-Thesis, (Pondicherry University, Puducherry, India, 1988). 
  7. [7] Vernold J. Vivin, M. Venkatachalam and M.M. Ali Akbar, A note on achromatic coloring of star graph families, Filomat 23(3) (2009) 251-255. doi:10.2298/FIL0903251V[Crossref][WoS] Zbl1265.05254

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