New Bounds on the Signed Total Domination Number of Graphs

Seyyed Mehdi Hosseini Moghaddam; Doost Ali Mojdeh; Babak Samadi; Lutz Volkmann

Discussiones Mathematicae Graph Theory (2016)

  • Volume: 36, Issue: 2, page 467-477
  • ISSN: 2083-5892

Abstract

top
In this paper, we study the signed total domination number in graphs and present new sharp lower and upper bounds for this parameter. For example by making use of the classic theorem of Turán [8], we present a sharp lower bound on Kr+1-free graphs for r ≥ 2. Applying the concept of total limited packing we bound the signed total domination number of G with δ(G) ≥ 3 from above by [...] . Also, we prove that γst(T) ≤ n − 2(s − s′) for any tree T of order n, with s support vertices and s′ support vertices of degree two. Moreover, we characterize all trees attaining this bound.

How to cite

top

Seyyed Mehdi Hosseini Moghaddam, et al. "New Bounds on the Signed Total Domination Number of Graphs." Discussiones Mathematicae Graph Theory 36.2 (2016): 467-477. <http://eudml.org/doc/277117>.

@article{SeyyedMehdiHosseiniMoghaddam2016,
abstract = {In this paper, we study the signed total domination number in graphs and present new sharp lower and upper bounds for this parameter. For example by making use of the classic theorem of Turán [8], we present a sharp lower bound on Kr+1-free graphs for r ≥ 2. Applying the concept of total limited packing we bound the signed total domination number of G with δ(G) ≥ 3 from above by [...] . Also, we prove that γst(T) ≤ n − 2(s − s′) for any tree T of order n, with s support vertices and s′ support vertices of degree two. Moreover, we characterize all trees attaining this bound.},
author = {Seyyed Mehdi Hosseini Moghaddam, Doost Ali Mojdeh, Babak Samadi, Lutz Volkmann},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {open packing; signed total domination number; total limited packing; tuple total domination number},
language = {eng},
number = {2},
pages = {467-477},
title = {New Bounds on the Signed Total Domination Number of Graphs},
url = {http://eudml.org/doc/277117},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Seyyed Mehdi Hosseini Moghaddam
AU - Doost Ali Mojdeh
AU - Babak Samadi
AU - Lutz Volkmann
TI - New Bounds on the Signed Total Domination Number of Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2016
VL - 36
IS - 2
SP - 467
EP - 477
AB - In this paper, we study the signed total domination number in graphs and present new sharp lower and upper bounds for this parameter. For example by making use of the classic theorem of Turán [8], we present a sharp lower bound on Kr+1-free graphs for r ≥ 2. Applying the concept of total limited packing we bound the signed total domination number of G with δ(G) ≥ 3 from above by [...] . Also, we prove that γst(T) ≤ n − 2(s − s′) for any tree T of order n, with s support vertices and s′ support vertices of degree two. Moreover, we characterize all trees attaining this bound.
LA - eng
KW - open packing; signed total domination number; total limited packing; tuple total domination number
UR - http://eudml.org/doc/277117
ER -

References

top
  1. [1] R. Gallant, G. Gunther, B. Hartnell and D.F. Rall, Limited packing in graphs, Dis- crete Appl. Math. 158 (2010) 1357-1364. doi:10.1016/j.dam.2009.04.014[Crossref] 
  2. [2] M.A. Henning, Signed total domination in graphs, Discrete Math. 278 (2004) 109-125. doi:10.1016/j.disc.2003.06.002[Crossref] 
  3. [3] M.A. Henning and A.P. Kazemi, k-tuple total domination in graphs, Discrete Appl. Math. 158 (2010) 1006-1011. doi:10.1016/j.dam.2010.01.009[Crossref][WoS] Zbl1210.05097
  4. [4] M.A. Henning and P.J. Slater, Open packing in graphs, J. Combin. Math. Combin. Comput. 28 (1999) 5-18. Zbl0922.05040
  5. [5] M.A. Henning and A. Yeo, Strong transversals in hypergraphs and double total domination in graphs, SIAM J. Discrete Math. 24 (2010) 1336-1355. doi:10.1137/090777001[Crossref][WoS] Zbl1221.05254
  6. [6] D.A. Mojdeh, B. Samadi and S.M. Hosseini Moghaddam, Limited packing vs tuple domination in graphs, Ars Combin. (to appear). Zbl1351.05170
  7. [7] E. Shan and T.C.E. Cheng, Remarks on the minus (signed) total domination in graphs, Discrete Math. 308 (2008) 3373-3380. doi:10.1016/j.disc.2007.06.015[WoS][Crossref] Zbl1169.05367
  8. [8] P. Turán, On an extremal problem in graph theory, Math. Fiz. Lapok 48 (1941) 436-452. 
  9. [9] D.B. West, Introduction to Graph Theory (Second Edition, Prentice Hall, USA, 2001). 
  10. [10] B. Zelinka, Signed total domination number of a graph, Czechoslovak Math. J. 51 (2001) 225-229. doi:10.1023/A:1013782511179[Crossref] Zbl0977.05096
  11. [11] W. Zhao, H. Wang and G. Xu, Total k-domination number in graphs, Int. J. Pure Appl. Math. 35 (2007) 235-242. 

NotesEmbed ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.