Geodesic
On the Total Graph of Mycielski Graphs, Central Graphs and Their Covering Numbers
Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 2, pp. 361-371

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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.
Keywords: total graph, central graph, middle graph, Mycielski graph, independence number, covering number, edge independence number, edge covering number, chromatic number, achromatic number 
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Patil, H.P.; Pandiya Raj, R. On the Total Graph of Mycielski Graphs, Central Graphs and Their Covering Numbers. Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 2, pp. 361-371. http://geodesic.mathdoc.fr/item/DMGT_2013_33_2_a9/