Total Domination Edge Critical Graphs

Creator(s)

L. C. Van Der Merwe, University of South Africa
C. M. Mynhardt, University of South Africa
T. W. Haynes, East Tennessee State University

Document Type

Article

Publication Date

11-1-1998

Description

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(Ḡ). In this introductory paper we give some basic results on γt-critical graphs, discuss properties of 3t-critical graphs, that is, γt-critical graphs with γt = 3, and characterise the 3t-critical graphs which contain cutvertices.

Citation Information

Van Der Merwe, L. C.; Mynhardt, C. M.; and Haynes, T. W.. 1998. Total Domination Edge Critical Graphs. Utilitas Mathematica. Vol.54 229-240. ISSN: 0315-3681