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

• Autorzy: H.P. Patil , R. Pandiya Raj
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

total graph; central graph; middle graph; Mycielski graph; independence number; covering number; edge independence number; edge covering number; chromatic number; achromatic number

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2013
• Tom: 33
• Numer: 2
• Strony: 361-371

Daty

wydano

2013-05-01

online

2013-04-13

Twórcy

autor

H.P. Patil

• Department of Mathematics Pondicherry Central University Puducherry - India

autor

R. Pandiya Raj

• Department of Mathematics Pondicherry Central University Puducherry - India

Bibliografia

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• [3] G. Kortsarz and S. Shende, Approximating the Achromatic Number Problem on Bipartite Graphs, (Springer Berlin / Heidelberg, 2003) LNCS Vol. 2832 385-396.[WoS]
• [4] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (London, MacMillan, 1976).
• [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]
• [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]

Identyfikatory

DOI

10.7151/dmgt.1670