# Intersection graph of gamma sets in the total graph

Discussiones Mathematicae Graph Theory (2012)

- Volume: 32, Issue: 2, page 341-356
- ISSN: 2083-5892

## Access Full Article

top## Abstract

top## How to cite

topT. Tamizh Chelvam, and T. Asir. "Intersection graph of gamma sets in the total graph." Discussiones Mathematicae Graph Theory 32.2 (2012): 341-356. <http://eudml.org/doc/270932>.

@article{T2012,

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 $I_\{Γ\}(ℤₙ)$.},

author = {T. Tamizh Chelvam, T. Asir},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {total graph; gamma sets; intersection graph; Hamiltonian; coloring; connectivity; domination number; independence number; clique number},

language = {eng},

number = {2},

pages = {341-356},

title = {Intersection graph of gamma sets in the total graph},

url = {http://eudml.org/doc/270932},

volume = {32},

year = {2012},

}

TY - JOUR

AU - T. Tamizh Chelvam

AU - T. Asir

TI - Intersection graph of gamma sets in the total graph

JO - Discussiones Mathematicae Graph Theory

PY - 2012

VL - 32

IS - 2

SP - 341

EP - 356

AB - 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 $I_{Γ}(ℤₙ)$.

LA - eng

KW - total graph; gamma sets; intersection graph; Hamiltonian; coloring; connectivity; domination number; independence number; clique number

UR - http://eudml.org/doc/270932

ER -

## References

top- [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. Zbl1174.13009
- [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. Zbl1158.13001
- [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. Zbl0941.05062
- [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). Zbl0938.05001
- [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. Zbl1193.05086
- [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. Zbl1193.05087
- [8] G. Chartrand and L. Lesniak, Graphs and Digraphs, (Chapman & Hall/CRC., 2000). Zbl0890.05001
- [9] G. Chartrand and P. Zhang, Chromatic Graph Theory, (CRC Press, 2009). Zbl1169.05001
- [10] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamental of Domination in Graphs, (Marcel Dekker Inc., 1998). Zbl0890.05002
- [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. Zbl1141.13008
- [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. Zbl0945.05003
- [13] T. Tamizh Chelvam and T. Asir, A note on total graph of ℤₙ, J. Discrete Math. Sci. Cryptography 14 (2011) 1-7. Zbl1261.05042
- [14] T. Tamizh Chelvam and T. Asir, Domination in the total graph on ℤₙ, J. Combin. Math. Combin. Comput., submitted. Zbl1297.05114
- [15] A.T. White, Graphs, Groups and Surfaces, (North-Holland, Amsterdam., 1973). Zbl0268.05102

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.