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Some Nordhaus - Gaddum Type Relations On Strong Efficient Dominating Sets

Year 2016, Volume: 5 Issue: 11, 4 - 16, 08.08.2016

Abstract

Let G = (V, E) be a simple graph with p vertices and q edges. A subset S of V(G) is called a strong (weak) efficient dominating set of G if for every vV(G),│Ns[v]∩S│=1(│Nw[v]∩S│=1).Ns(v) ={u V(G) uv E(G), deg(u) ≥ deg(v)}.The minimum cardinality of a strong (weak) efficient dominating set G is called strong (weak) efficient domination number of G and is denoted by γse (γwe ). A graph G is strong efficient if there exists a strong efficient dominating set of G. In this paper, the authors introduced a new parameter called the number of strong efficient dominating sets of a graph G denoted by # γse (G) and studied some Nordhaus- Gaddum type relations on strong efficient domination number of a graph and its derived graph. The relation between the number of strong efficient dominating sets of a graph and its derived graph is also studied

References

  • Bange. D.W, Barkauskas. A.E. and Slater. P.J., Efficient dominating sets in graphs, Application of Discrete Mathematics, 189 – 199, SIAM, Philadephia (1988).
  • Harary. F., Graph Theory, Addison – Wesley (1969).
  • Haynes. T W., Stephen T. Hedetniemi, Peter J. Slater. Fundamentals of domination in graphs. Advanced Topics, Marcel Dekker, Inc, New York (1998).
  • Meena.N., Subramanian.A.., Swaminathan.V., Graphs in which Upper Strong Efficient Domination Number Equals the Independent Number, International Journal of Engineering and Science Invention, 32-39,Vol 2, Issue 12, December 2013.
  • Meena.N., Subramanian.A.., Swaminathan.V., Strong Efficient Domination in Graphs, International Journal of Innovative Science, Engineering & Technology, 172-177, Vol.1 Issue 4, June 2014.
  • Sampathkumar.E and Pushpa Latha.L. Strong weak domination and domination balance in a graph, Discrete Math., 161: 235 – 242 (1996).
  • S.K.vaidya and P.L.Vihol, Fibonacci and Super Fibonacci graceful labeling of some graphs, Studies in Mathematical Sciences,Vol.2,No.2,(2011), 24-35.
Year 2016, Volume: 5 Issue: 11, 4 - 16, 08.08.2016

Abstract

References

  • Bange. D.W, Barkauskas. A.E. and Slater. P.J., Efficient dominating sets in graphs, Application of Discrete Mathematics, 189 – 199, SIAM, Philadephia (1988).
  • Harary. F., Graph Theory, Addison – Wesley (1969).
  • Haynes. T W., Stephen T. Hedetniemi, Peter J. Slater. Fundamentals of domination in graphs. Advanced Topics, Marcel Dekker, Inc, New York (1998).
  • Meena.N., Subramanian.A.., Swaminathan.V., Graphs in which Upper Strong Efficient Domination Number Equals the Independent Number, International Journal of Engineering and Science Invention, 32-39,Vol 2, Issue 12, December 2013.
  • Meena.N., Subramanian.A.., Swaminathan.V., Strong Efficient Domination in Graphs, International Journal of Innovative Science, Engineering & Technology, 172-177, Vol.1 Issue 4, June 2014.
  • Sampathkumar.E and Pushpa Latha.L. Strong weak domination and domination balance in a graph, Discrete Math., 161: 235 – 242 (1996).
  • S.K.vaidya and P.L.Vihol, Fibonacci and Super Fibonacci graceful labeling of some graphs, Studies in Mathematical Sciences,Vol.2,No.2,(2011), 24-35.
There are 7 citations in total.

Details

Journal Section Articles
Authors

K Murugan This is me

N Meena This is me

Publication Date August 8, 2016
Published in Issue Year 2016 Volume: 5 Issue: 11

Cite

APA Murugan, K., & Meena, N. (2016). Some Nordhaus - Gaddum Type Relations On Strong Efficient Dominating Sets. Journal of New Results in Science, 5(11), 4-16.
AMA Murugan K, Meena N. Some Nordhaus - Gaddum Type Relations On Strong Efficient Dominating Sets. JNRS. October 2016;5(11):4-16.
Chicago Murugan, K, and N Meena. “Some Nordhaus - Gaddum Type Relations On Strong Efficient Dominating Sets”. Journal of New Results in Science 5, no. 11 (October 2016): 4-16.
EndNote Murugan K, Meena N (October 1, 2016) Some Nordhaus - Gaddum Type Relations On Strong Efficient Dominating Sets. Journal of New Results in Science 5 11 4–16.
IEEE K. Murugan and N. Meena, “Some Nordhaus - Gaddum Type Relations On Strong Efficient Dominating Sets”, JNRS, vol. 5, no. 11, pp. 4–16, 2016.
ISNAD Murugan, K - Meena, N. “Some Nordhaus - Gaddum Type Relations On Strong Efficient Dominating Sets”. Journal of New Results in Science 5/11 (October 2016), 4-16.
JAMA Murugan K, Meena N. Some Nordhaus - Gaddum Type Relations On Strong Efficient Dominating Sets. JNRS. 2016;5:4–16.
MLA Murugan, K and N Meena. “Some Nordhaus - Gaddum Type Relations On Strong Efficient Dominating Sets”. Journal of New Results in Science, vol. 5, no. 11, 2016, pp. 4-16.
Vancouver Murugan K, Meena N. Some Nordhaus - Gaddum Type Relations On Strong Efficient Dominating Sets. JNRS. 2016;5(11):4-16.


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