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Doost Ali Mojdeh

Doost Ali Mojdeh

Academic rank: Professor
ORCID:
Education: PhD.
ScopusId:
Faculty: Faculty of Mathematical Sciences
Address: Department of Mathematics, University of Mazandaran, Babolsar, Iran
Phone: 011-35302448

Research

Title
Liars dominating sets in graphs,
Type
JournalPaper
Keywords
Liar’s dominatio Double domination Packing numberr-partite graph
Year
2016
Journal DISCRETE APPLIED MATHEMATICS
DOI
Researchers Abdollah Alimadadi ، Mustapha Chellali ، Doost Ali Mojdeh

Abstract

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