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

100%
Patil H. P., Pandiya Raj R.
Discussiones Mathematicae Graph Theory
|
2013
|
tom 33
|
nr 2
361-371
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.
2
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On degree sets and the minimum orders in bipartite graphs

100%
Manoussakis Y., Patil H. P.
Discussiones Mathematicae Graph Theory
|
2014
|
tom 34
|
nr 2
383-390
EN
For any simple graph G, let D(G) denote the degree set {degG(v) : v ∈ V (G)}. Let S be a finite, nonempty set of positive integers. In this paper, we first determine the families of graphs G which are unicyclic, bipartite satisfying D(G) = S, and further obtain the graphs of minimum orders in such families. More general, for a given pair (S, T) of finite, nonempty sets of positive integers of the same cardinality, it is shown that there exists a bipartite graph B(X, Y ) such that D(X) = S, D(Y ) = T and the minimum orders of different types are obtained for such graphs
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A Note on Total Graphs

71%
Forouhandeh S. F., Jafari Rad N., Vaqari Motlagh B. H., Patil H. P., Pandiya Raj R.
Discussiones Mathematicae Graph Theory
|
2015
|
tom 35
|
nr 3
585-587
EN
Erratum Identification and corrections of the existing mistakes in the paper On the total graph of Mycielski graphs, central graphs and their covering numbers, Discuss. Math. Graph Theory 33 (2013) 361-371.
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