Geodesic
Intersection graph of gamma sets in the total graph
Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 2, pp. 341-356

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In this paper, we consider the intersection graph I_Γ(ℤₙ) of gamma sets in the total graph on ℤₙ. We characterize the values of n for which I_Γ(ℤₙ) is complete, bipartite, cycle, chordal and planar. Further, we prove that I_Γ(ℤₙ) is an Eulerian, Hamiltonian and as well as a pancyclic graph. Also we obtain the value of the independent number, the clique number, the chromatic number, the connectivity and some domination parameters of I_Γ(ℤₙ).
Keywords: total graph, gamma sets, intersection graph, Hamiltonian, coloring, connectivity, domination number 
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     author = {Chelvam, T. and Asir, T.},
     title = {Intersection graph of gamma sets in the total graph},
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Chelvam, T.; Asir, T. Intersection graph of gamma sets in the total graph. Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 2, pp. 341-356. http://geodesic.mathdoc.fr/item/DMGT_2012_32_2_a12/