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2012 | 32 | 2 | 341-356
Tytuł artykułu

Intersection graph of gamma sets in the total graph

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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 $I_{Γ}(ℤₙ)$.
Wydawca
Rocznik
Tom
32
Numer
2
Strony
341-356
Opis fizyczny
Daty
wydano
2012
otrzymano
2011-02-04
poprawiono
2011-06-17
zaakceptowano
2011-06-20
Twórcy
  • Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli- 627 012, Tamil Nadu, India
autor
  • Department of Mathematics Manonmaniam Sundaranar University, Tirunelveli- 627 012, Tamil Nadu, India
Bibliografia
  • [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 ℤₙ, J. Discrete Math. Sci. Cryptography 14 (2011) 1-7.
  • [14] T. Tamizh Chelvam and T. Asir, Domination in the total graph on ℤₙ, J. Combin. Math. Combin. Comput., submitted.
  • [15] A.T. White, Graphs, Groups and Surfaces, (North-Holland, Amsterdam., 1973).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1611
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