A characterization of (γₜ,γ₂)-trees

You Lu; Xinmin Hou; Jun-Ming Xu; Ning Li

Discussiones Mathematicae Graph Theory (2010)

  • Volume: 30, Issue: 3, page 425-435
  • ISSN: 2083-5892

Abstract

top
Let γₜ(G) and γ₂(G) be the total domination number and the 2-domination number of a graph G, respectively. It has been shown that: γₜ(T) ≤ γ₂(T) for any tree T. In this paper, we provide a constructive characterization of those trees with equal total domination number and 2-domination number.

How to cite

top

You Lu, et al. "A characterization of (γₜ,γ₂)-trees." Discussiones Mathematicae Graph Theory 30.3 (2010): 425-435. <http://eudml.org/doc/270837>.

@article{YouLu2010,
abstract = {Let γₜ(G) and γ₂(G) be the total domination number and the 2-domination number of a graph G, respectively. It has been shown that: γₜ(T) ≤ γ₂(T) for any tree T. In this paper, we provide a constructive characterization of those trees with equal total domination number and 2-domination number.},
author = {You Lu, Xinmin Hou, Jun-Ming Xu, Ning Li},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {domination; total domination; 2-domination; (λ,μ)-tree; -tree},
language = {eng},
number = {3},
pages = {425-435},
title = {A characterization of (γₜ,γ₂)-trees},
url = {http://eudml.org/doc/270837},
volume = {30},
year = {2010},
}

TY - JOUR
AU - You Lu
AU - Xinmin Hou
AU - Jun-Ming Xu
AU - Ning Li
TI - A characterization of (γₜ,γ₂)-trees
JO - Discussiones Mathematicae Graph Theory
PY - 2010
VL - 30
IS - 3
SP - 425
EP - 435
AB - Let γₜ(G) and γ₂(G) be the total domination number and the 2-domination number of a graph G, respectively. It has been shown that: γₜ(T) ≤ γ₂(T) for any tree T. In this paper, we provide a constructive characterization of those trees with equal total domination number and 2-domination number.
LA - eng
KW - domination; total domination; 2-domination; (λ,μ)-tree; -tree
UR - http://eudml.org/doc/270837
ER -

References

top
  1. [1] M. Blidia, M. Chellalia and T.W. Haynes, Characterizations of trees with equal paired and double domination numbers, Discrete Math. 306 (2006) 1840-1845, doi: 10.1016/j.disc.2006.03.061. Zbl1100.05068
  2. [2] M. Blidia, M. Chellali and L. Volkmann, Some bounds on the p-domination number in trees, Discrete Math. 306 (2006) 2031-2037, doi: 10.1016/j.disc.2006.04.010. Zbl1100.05069
  3. [3] E.J. Cockayne, R.M. Dawes and S.T. Hedetniemi, Total domination in graphs, Networks 10 (1980) 211-219, doi: 10.1002/net.3230100304. Zbl0447.05039
  4. [4] E.J. Cockayne, O. Favaron, C.M. Mynhardt and J. Puech, A characterization of (γ,i)-trees, J. Graph Theory 34 (2000) 277-292, doi: 10.1002/1097-0118(200008)34:4<277::AID-JGT4>3.0.CO;2-# Zbl0949.05059
  5. [5] G. Chartrant and L. Lesniak, Graphs & Digraphs, third ed. (Chapman & Hall, London, 1996). 
  6. [6] J.F. Fink and M.S. Jacobson, n-Domination in graphs, in: Y. Alavi, A.J. Schwenk (eds.), Graph Theory with Applications to Algorithms and Computer Science (Wiley, New York, 1985) 283-300. Zbl0573.05049
  7. [7] F. Harary and M. Livingston, Characterization of trees with equal domination and independent domination numbers, Congr. Numer. 55 (1986) 121-150. Zbl0647.05020
  8. [8] T.W. Haynes, S.T. Hedetniemi, M.A. Henning and P.J. Slater, H-forming sets in graphs, Discrete Math. 262 (2003) 159-169, doi: 10.1016/S0012-365X(02)00496-X. Zbl1017.05082
  9. [9] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (New York, Marcel Deliker, 1998). Zbl0890.05002
  10. [10] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics (New York, Marcel Deliker, 1998). Zbl0883.00011
  11. [11] T.W. Haynes, M.A. Henning and P.J. Slater, Strong quality of domination parameters in trees, Discrete Math. 260 (2003) 77-87, doi: 10.1016/S0012-365X(02)00451-X. Zbl1020.05051
  12. [12] M.A. Henning, A survey of selected recently results on total domination in graphs, Discrete Math. 309 (2009) 32-63, doi: 10.1016/j.disc.2007.12.044. 
  13. [13] X. Hou, A characterization of (2γ,γₚ)-trees, Discrete Math. 308 (2008) 3420-3426, doi: 10.1016/j.disc.2007.06.034. Zbl1165.05023

NotesEmbed ?

top

You must be logged in to post comments.