Discussiones Mathematicae Graph Theory 32(2) (2012) 341-356
doi: 10.7151/dmgt.1611

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Intersection Graph of Gamma Sets in the Total Graph

T. Tamizh Chelvam
and
T. Asir

Department of Mathematics
Manonmaniam Sundaranar University
Tirunelveli- 627 012, Tamil Nadu, India

Abstract

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

2010 Mathematics Subject Classification: 05C40,05C45, 05C69.

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Received 4 February 2011
Revised 17 June 2011
Accepted 20 June 2011