Total domination edge critical graphs with maximum diameter

Lucas C. van der Merwe; Cristine M. Mynhardt; Teresa W. Haynes

Discussiones Mathematicae Graph Theory (2001)

  • Volume: 21, Issue: 2, page 187-205
  • ISSN: 2083-5892

Abstract

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Denote the total domination number of a graph G by γₜ(G). A graph G is said to be total domination edge critical, or simply γₜ-critical, if γₜ(G+e) < γₜ(G) for each edge e ∈ E(G̅). For 3ₜ-critical graphs G, that is, γₜ-critical graphs with γₜ(G) = 3, the diameter of G is either 2 or 3. We characterise the 3ₜ-critical graphs G with diam G = 3.

How to cite

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Lucas C. van der Merwe, Cristine M. Mynhardt, and Teresa W. Haynes. "Total domination edge critical graphs with maximum diameter." Discussiones Mathematicae Graph Theory 21.2 (2001): 187-205. <http://eudml.org/doc/270384>.

@article{LucasC2001,
abstract = {Denote the total domination number of a graph G by γₜ(G). A graph G is said to be total domination edge critical, or simply γₜ-critical, if γₜ(G+e) < γₜ(G) for each edge e ∈ E(G̅). For 3ₜ-critical graphs G, that is, γₜ-critical graphs with γₜ(G) = 3, the diameter of G is either 2 or 3. We characterise the 3ₜ-critical graphs G with diam G = 3.},
author = {Lucas C. van der Merwe, Cristine M. Mynhardt, Teresa W. Haynes},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {total domination number; edge critical},
language = {eng},
number = {2},
pages = {187-205},
title = {Total domination edge critical graphs with maximum diameter},
url = {http://eudml.org/doc/270384},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Lucas C. van der Merwe
AU - Cristine M. Mynhardt
AU - Teresa W. Haynes
TI - Total domination edge critical graphs with maximum diameter
JO - Discussiones Mathematicae Graph Theory
PY - 2001
VL - 21
IS - 2
SP - 187
EP - 205
AB - Denote the total domination number of a graph G by γₜ(G). A graph G is said to be total domination edge critical, or simply γₜ-critical, if γₜ(G+e) < γₜ(G) for each edge e ∈ E(G̅). For 3ₜ-critical graphs G, that is, γₜ-critical graphs with γₜ(G) = 3, the diameter of G is either 2 or 3. We characterise the 3ₜ-critical graphs G with diam G = 3.
LA - eng
KW - total domination number; edge critical
UR - http://eudml.org/doc/270384
ER -

References

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  1. [1] E. Cockayne, R. Dawes and S. Hedetniemi, Total domination in graphs, Networks 10 (1980) 211-219, doi: 10.1002/net.3230100304. Zbl0447.05039
  2. [2] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, Inc., New York, 1998). Zbl0890.05002
  3. [3] T.W. Haynes, C.M. Mynhardt and L.C. van der Merwe, Total domination edge critical graphs, Utilitas Math. 54 (1998) 229-240. Zbl0918.05069
  4. [4] T.W. Haynes, C.M. Mynhardt and L.C. van der Merwe, Criticality index of total domination, Congr. Numer. 131 (1998) 67-73. Zbl0951.05081
  5. [5] D.P. Sumner and P. Blitch, Domination critical graphs, J. Combin. Theory (B) 34 (1983) 65-76, doi: 10.1016/0095-8956(83)90007-2. Zbl0512.05055
  6. [6] D.P. Sumner and E. Wojcicka, Graphs critical with respect to the domination number, Domination in Graphs: Advanced Topics (Chapter 16), T.W. Haynes, S.T. Hedetniemi and P.J. Slater, eds. (Marcel Dekker, Inc., New York, 1998). Zbl0891.05043

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