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Discrete Mathematics and Combinatorics Commons™
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Full-Text Articles in Discrete Mathematics and Combinatorics
Total Domination Dot Critical And Dot Stable Graphs., Stephanie Anne Marie Mcmahon
Total Domination Dot Critical And Dot Stable Graphs., Stephanie Anne Marie Mcmahon
Electronic Theses and Dissertations
Two vertices are said to be identifed if they are combined to form one vertex whose neighborhood is the union of their neighborhoods. A graph is total domination dot-critical if identifying any pair of adjacent vertices decreases the total domination number. On the other hand, a graph is total domination dot-stable if identifying any pair of adjacent vertices leaves the total domination number unchanged. Identifying any pair of vertices cannot increase the total domination number. Further we show it can decrease the total domination number by at most two. Among other results, we characterize total domination dot-critical trees with total …
Double Domination Edge Critical Graphs., Derrick Wayne Thacker
Double Domination Edge Critical Graphs., Derrick Wayne Thacker
Electronic Theses and Dissertations
In a graph G=(V,E), a subset S ⊆ V is a double dominating set if every vertex in V is dominated at least twice. The minimum cardinality of a double dominating set of G is the double domination number. A graph G is double domination edge critical if for any edge uv ∈ E(G̅), the double domination number of G+uv is less than the double domination number of G. We investigate properties of double domination edge critical graphs. In particular, we characterize the double domination edge critical trees and …