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

Discussiones Mathematicae Graph Theory (2013)

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

## Access Full Article

top## Abstract

top## How to cite

topH.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

top- [1] F. Harary, Graph Theory (Narosa Publishing Home, 1969).
- [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] 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] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (London, MacMillan, 1976). Zbl1226.05083
- [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] Ramakrishnan, MPhil-Thesis, (Pondicherry University, Puducherry, India, 1988).
- [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