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Equitable critical graphs

Discrete Mathematics, Algorithms and Applications, 2022
A proper vertex coloring of a graph [Formula: see text] is equitable if the sizes of any two color classes differ by at most one. The equitable chromatic number of a graph [Formula: see text], denoted by [Formula: see text], is the minimum [Formula: see text] such that [Formula: see text] is equitably [Formula: see text]-colorable.
Loura Jency, Benedict Michael Raj
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Vertex domination‐critical graphs

Networks, 1988
AbstractA dominating set in a graph G is a set of vertices D such that every vertex of G is either in D or is adjacent some vertex of D. The domination number Γ(G) of G is the minimum cardinality of any dominating set. A graph is vertex domination‐critical if the removal of any vertex decreases its domination number.
Brigham, Robert C., Chinn, Phyllis Z., Dutton, Ronald D.   +2 more
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Vertex domination‐critical graphs

Networks, 1995
AbstractA graph G is vertex domination‐critical if for any vertex v of G the domination number of G ‐ v is less than the domination number of G. If such a graph G has domination number γ, it is called γ‐critical. Brigham et al. studied γ‐critical graphs and posed the following questions: (1) If G is a γ‐critical graph, is |V| ≥ (δ + 1)(γ ‐ 1) + 1?(2 ...
Fulman, Jason, Hanson, Denis, MacGillivray, Gary   +2 more
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Equimatchable factor‐critical graphs

Journal of Graph Theory, 1986
AbstractA simple graph G(X, E) is factor‐critical if the induced subgraph 〈X – x〉 admits a perfect matching for every vertex x of G. It is equimatchable if every maximal matching of G is maximum. The equimatchable non‐factor‐critical graphs have been studied by Lesk, Plummer, and Pulleyblank.
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Critically cochromatic graphs

Journal of Graph Theory, 1989
AbstractA graph G is critically n‐cochromatic if (its cochromatic number) z(G) = n and z(G ‐ v) = n ‐ 1 for every vertex v of G. Properties of critically n‐cochromatic graphs are discussed and we also construct graphs that are critically n‐chromatic and critically n‐cochromatic.
Broere, Izak, Burger, Marieta
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Roman Domination Dot-critical Graphs

Graphs and Combinatorics, 2012
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Jafari Rad, Nader, Volkmann, Lutz
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