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## Discussiones Mathematicae Graph Theory

2011 | 31 | 1 | 197-202
Tytuł artykułu

### A characterization of locating-total domination edge critical graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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 of G. A graph G is said to be a locating-total domination edge removal critical graph, or just a $γ_L^{t+}$-ER-critical graph, if $γ_L^t(G-e) > γ_L^t(G)$ for all e non-pendant edge of E. The purpose of this paper is to characterize the class of $γ_L^{t+}$-ER-critical graphs.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
197-202
Opis fizyczny
Daty
wydano
2011
otrzymano
2008-12-08
poprawiono
2009-12-20
zaakceptowano
2010-01-21
Twórcy
autor
• LAMDA-RO, Department of Mathematics, University of Blida, B.P. 270, Blida, Algeria
autor
• Department R-O, University of Algiers, Algeria
Bibliografia
• [1] M. Blidia and W. Dali, A characterization of a locating-domination edge critical graphs, Australasian J. Combin. 44 (2009) 297-300.
• [2] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998).
• [3] D.P. Sumner and P. Blitch, Domination critical graphs, J. Combin. Theory (B) 34 (1983) 65-76, doi: 10.1016/0095-8956(83)90007-2.
• [4] T.W. Haynes, M.A. Henning and J. Howard, Locating and total dominating sets in trees, Discrete Appl. Math. 154 (2006) 1293-1300, doi: 10.1016/j.dam.2006.01.002.
Typ dokumentu
Bibliografia
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