ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

Journal Impact Factor (JIF 2023): 0.5

5-year Journal Impact Factor (2023): 0.6

CiteScore (2023): 2.2

SNIP (2023): 0.681

Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 32(2) (2012) 341-356

Intersection Graph of Gamma Sets in the Total Graph

T. Tamizh Chelvam
T. Asir

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


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.


[1]S. Akbari, D. Kiani, F. Mohammadi and S. Moradi, The total graph and regular graph of a commutative ring, J. Pure Appl. Algebra 213 (2009) 2224--2228, doi: 10.1016/j.jpaa.2009.03.013.
[2]D.F. Anderson and A. Badawi, The total graph of a commutative ring, J. Algebra 320 (2008) 2706--2719, doi: 10.1016/j.jalgebra.2008.06.028.
[3]D.F. Anderson and P.S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra 217 (1999) 434--447, doi: 10.1006/jabr.1998.7840.
[4]N. Ashrafia, H.R. Maimanibc, M.R. Pournakicd and S. Yassemie, Unit graphs associated with rings, Comm. Algebra 38 (2010) 2851?-2871, doi: 10.1080/00927870903095574.
[5]R. Balakrishnan and K. Ranganathan, A text book of Graph Theory, (Springer, 2000).
[6]I. Chakrabarty, S. Ghosh, T.K. Mukherjee and M.K. Sen, Intersection graphs of ideals of rings, Electronic Notes in Discrete Math. 23 (2005) 23--32, doi: 10.1016/j.endm.2005.06.104.
[7]I. Chakrabarty, S. Ghosh, T.K. Mukherjee and M.K. Sen, Intersection graphs of ideals of rings, Discrete Math. 309 (2009) 5381-5392, doi: 10.1016/j.disc.2008.11.034.
[8]G. Chartrand and L. Lesniak, Graphs and Digraphs, (Chapman & Hall/CRC., 2000).
[9]G. Chartrand and P. Zhang, Chromatic Graph Theory, (CRC Press, 2009).
[10]T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamental of Domination in Graphs, (Marcel Dekker Inc., 1998).
[11]H.R. Maimani, M. Salimi, A. Sattari and S. Yassemi, Comaximal graph of commutative rings, J. Algebra 319 (2008) 1801--1808, doi: 10.1016/j.jalgebra.2007.02.003.
[12]T.A. McKee and F.R. McMorris, Topics in Intersection Graph Theory, (SIAM Monographs on Discrete Math. Applications., 1999), doi: 10.1137/1.9780898719802.
[13]T. Tamizh Chelvam and T. Asir, A note on total graph of n, J. Discrete Math. Sci. Cryptography 14 (2011) 1--7.
[14]T. Tamizh Chelvam and T. Asir, Domination in the total graph on n, J. Combin. Math. Combin. Comput., submitted.
[15]A.T. White, Graphs, Groups and Surfaces, (North-Holland, Amsterdam., 1973).

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