On the Total Graph of Mycielski Graphs, Central Graphs and Their Covering Numbers
H.P. Patil ; R. Pandiya Raj
Discussiones Mathematicae Graph Theory, Tome 33 (2013), p. 361-371 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:268246 
@article{bwmeta1.element.doi-10_7151_dmgt_1670,
     author = {H.P. Patil and R. Pandiya Raj},
     title = {On the Total Graph of Mycielski Graphs, Central Graphs and Their Covering Numbers},
     journal = {Discussiones Mathematicae Graph Theory},
     volume = {33},
     year = {2013},
     pages = {361-371},
     zbl = {1297.05199},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1670}
}

H.P. Patil; R. Pandiya Raj. On the Total Graph of Mycielski Graphs, Central Graphs and Their Covering Numbers. Discussiones Mathematicae Graph Theory, Tome 33 (2013) pp. 361-371. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1670/

[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] | Zbl 1266.68230

[4] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (London, MacMillan, 1976). | Zbl 1226.05083

[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] | Zbl 1267.05227

[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] | Zbl 1265.05254