Discussiones Mathematicae Graph Theory 33(2) (2013) 361-371
doi: 10.7151/dmgt.1670

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

H.P. Patil and R. Pandiya Raj

Department of Mathematics
Pondicherry Central University
Puducherry - India


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 complete-graph 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.

Keywords: total graph, central graph, middle graph, Mycielski graph, independence number, covering number, edge independence number, edge covering number, chromatic number, achromatic number

2010 Mathematics Subject Classification: 05C76, 05C69.


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Received 16 May 2011
Revised 2 May 2012
Accepted 2 May 2012