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A characterization of locating-total domination edge critical graphs

Mostafa BlidiaWidad Dali — 2011

Discussiones Mathematicae Graph Theory

For a graph G = (V,E) without isolated vertices, a subset D of vertices of V is a total dominating set (TDS) of G if every vertex in V is adjacent to a vertex in D. The total domination number γₜ(G) is the minimum cardinality of a TDS of G. A subset D of V which is a total dominating set, is a locating-total dominating set, or just a LTDS of G, if for any two distinct vertices u and v of V(G)∖D, N G ( u ) D N G ( v ) D . The locating-total domination number γ L t ( G ) is the minimum cardinality of a locating-total dominating set...

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