DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 21(1) (2001) 187-205
DOI: 10.7151/dmgt.1143

TOTAL DOMINATION EDGE CRITICAL GRAPHS WITH MAXIMUM DIAMETER

Lucas C. van der Merwe, Cristine M. Mynhardt

University of South Africa
Pretoria, South Africa

Teresa W. Haynes

East Tennessee State University
Johnson City, TN 37614 USA

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([`G]). 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.

References

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Received 5 October 2000