2024 : 4 : 26
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
NEW BOUNDS ON THE SIGNED TOTAL DOMINATION NUMBER OF GRAPHS
Type
JournalPaper
Keywords
open packing, signed total domination number, total limited packing, tuple total domination number.
Year
2016
Journal Discussiones Mathematicae Graph Theory
DOI
Researchers Doost Ali Mojdeh ، Seyed Mehdi Hosseini Moghaddam ، Babak Samadi ، Lutz Volkmann

Abstract

In this paper, we study the signed total domination number in graphs and present new sharp lower and upper bounds for this parameter. For example by making use of the classic theorem of Tur\'{a}n \cite{t}, we present a sharp lower bound on $K‎_{r+1}‎$-free graphs for $r‎\geq2‎$. Applying the concept of total limited packing we bound the signed total domination number of $G$ with $‎\delta(G)‎\geq3‎‎$ from above by $n-2‎\lfloor‎\frac{2‎\rho‎_{o}(G)‎‎+‎\delta-3‎}{2}‎‎\rfloor‎‎‎$. Also, we prove that $\gamma_{st}(T)‎\leq n-2(s-s')‎$ for any tree $T$ of order $n$, with $s$ support vertices and $s'$ support vertices of degree two. Moreover, we characterize all trees attaining this bound.