June 10, 2023
Doost Ali Mojdeh

Doost Ali Mojdeh

Degree: Professor
Address: Department of Mathematics, University of Mazandaran, Babolsar, Iran
Education: Ph.D in Mathematics (Graph Theory and Combinatorics)
Phone: 011-35302448
Faculty: Faculty of Mathematical Sciences


Title Liars dominating sets in graphs,
Type Article
Liar’s dominatio Double domination Packing numberr-partite graph
DOI http://dx.doi.org/10.1016/j.dam.2016.04.023
Researchers Abdollah Alimadadi (First researcher) , Mustapha Chellali (Second researcher) , Doost Ali Mojdeh (Third researcher)


A set L ⊆ V of a graph G = (V, E) is a liar’s dominating set if (1) for every vertex u ∈ V, |N[u] ∩ L| ≥ 2 and (2) for every pair u, v ∈ V of distinct vertices, |(N[u] ∪ N[v]) ∩ L| ≥ 3. In this paper, we first provide a characterization of graphs G with γLR(G) = |V| as well as the trees T with γLR(T ) = |V| − 1. Then we present some bounds on the liar’s domination number, especially an upper bound for the ratio between the liar’s domination number and the double domination number is established for connected graphs with girth at least five. Finally, we determine the exact value of the liar’s domination number for the complete r-partite graphs