Open AccessTotal Domination Edge Critical Graphs with Maximum Diameter
Author(s) -
Teresa W. Haynes,
Christina M. Mynhardt,
Lucas C. van der Merwe
Publication year - 2001
Publication title -
discussiones mathematicae graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.476
H-Index - 19
eISSN - 2083-5892
pISSN - 1234-3099
DOI - 10.7151/dmgt.1143
Subject(s) - mathematics , combinatorics , enhanced data rates for gsm evolution , domination analysis , graph , vertex (graph theory) , computer science , artificial intelligence
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 γtcritical, 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.
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