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Domination critical graphs with higher independent domination numbers
Author(s) -
Ao S.,
Cockayne E. J.,
MacGillivray G.,
Mynhardt C. M.
Publication year - 1996
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/(sici)1097-0118(199605)22:1<9::aid-jgt2>3.0.co;2-s
Subject(s) - combinatorics , mathematics , conjecture , domination analysis , graph , discrete mathematics , vertex (graph theory)
We show that for each k ≥ 4 there exists a connected k ‐domination critical graph with independent domination number exceeding k , thus disproving a conjecture of Sumner and Blitch ( J. Combinatorial Theory B 34 (1983), 65–76) in all cases except k = 3. © 1996 John Wiley & Sons, Inc.