2016
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2
2
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A full NesterovTodd step interiorpoint method for circular cone optimization
2
2
In this paper, we present a full Newton step feasible interiorpointmethod for circular cone optimization by using Euclidean Jordanalgebra. The search direction is based on the NesterovTodd scalingscheme, and only fullNewton step is used at each iteration.Furthermore, we derive the iteration bound that coincides with thecurrently best known iteration bound for smallupdate methods.
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83
102


Behrouz
Kheirfam
Azarbaijan Shahid Madani University
Azarbaijan Shahid Madani University
Iran
b.kheirfam@azaruniv.edu
Circular cone optimization
FullNewton step
Interiorpoint methods
Euclidean Jordan algebra
Hypoefficient domination and hypounique domination
2
2
For a graph $G$ let $gamma (G)$ be its domination number. We define a graph G to be (i) a hypoefficient domination graph (or a hypo$mathcal{ED}$ graph) if $G$ has no efficient dominating set (EDS) but every graph formed by removing a single vertex from $G$ has at least one EDS, and (ii) a hypounique domination graph (a hypo$mathcal{UD}$ graph) if $G$ has at least two minimum dominating sets, but $Gv$ has a unique minimum dominating set for each $vin V(G)$. We show that each hypo$mathcal{UD}$ graph $G$ of order at least $3$ is connected and $gamma(Gv) < gamma(G)$ for all $v in V$. We obtain a tight upper bound on the order of a hypo$mathcal{P}$ graph in terms of the domination number and maximum degree of the graph, where $mathcal{P} in {mathcal{UD}, mathcal{ED}}$. Families of circulant graphs, which achieve these bounds, are presented. We also prove that the bondage number of any hypo$mathcal{UD}$ graph is not more than the minimum degree plus one.
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103
116


Vladimir
Samodivkin
University of Architecture, Civil Еngineering and Geodesy;
Department of Mathematics
University of Architecture, Civil Еngineering
Bulgaria
vl.samodivkin@gmail.com
domination number
efficient domination
unique domination
hypoproperty
The sumannihilating essential ideal graph of a commutative ring
2
2
Let $R$ be a commutative ring with identity. An ideal $I$ of a ring $R$is called an annihilating ideal if there exists $rin Rsetminus {0}$ such that $Ir=(0)$ and an ideal $I$ of$R$ is called an essential ideal if $I$ has nonzero intersectionwith every other nonzero ideal of $R$. Thesumannihilating essential ideal graph of $R$, denoted by $mathcal{AE}_R$, isa graph whose vertex set is the set of all nonzero annihilating ideals and twovertices $I$ and $J$ are adjacent whenever ${rm Ann}(I)+{rmAnn}(J)$ is an essential ideal. In this paper we initiate thestudy of the sumannihilating essential ideal graph. We first characterize all rings whose sumannihilating essential ideal graph are stars or complete graphs and then establish sharp bounds on domination number of this graph. Furthermore determine all isomorphism classes of Artinian rings whose sumannihilating essential ideal graph has genus zero or one.
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117
135


Abbas
Alilou
Azarbaijan Shahid Madani University
Azarbaijan Shahid Madani University
Iran
a_alilou@azaruniv.edu


Jafar
Amjadi
Azarbaijan Shahid Madani University
Azarbaijan Shahid Madani University
Iran
jamjadi@azaruniv.edu
Commutative rings
annihilating ideal
essential ideal
genus of a graph
On trees and the multiplicative sum Zagreb index
2
2
For a graph $G$ with edge set $E(G)$, the multiplicative sum Zagreb index of $G$ is defined as$Pi^*(G)=Pi_{uvin E(G)}[d_G(u)+d_G(v)]$, where $d_G(v)$ is the degree of vertex $v$ in $G$.In this paper, we first introduce some graph transformations that decreasethis index. In application, we identify the fourteen class of trees, with the first through fourteenth smallest multiplicative sum Zagreb indeces among all trees of order $ngeq 13$.
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137
148


Mehdi
Eliasi
Dept. of Mathematics, Khansar Faculty of Mathematics and Computer Science,
Khansar, Iran,
Dept. of Mathematics, Khansar Faculty of
Iran
m.elyasi@khansarcmc.ac.ir


Ali
Ghalavand
Dept. of Mathematics, Khansar Faculty of Mathematics and Computer Science,
Khansar, Iran
Dept. of Mathematics, Khansar Faculty of
Iran
ali797ghalavand@gmail.com
Multiplicative Sum Zagreb Index
Graph Transformation
Branching Point
trees
Twin minus domination in directed graphs
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2
Let $D=(V,A)$ be a finite simple directed graph. A function$f:Vlongrightarrow {1,0,1}$ is called a twin minus dominatingfunction (TMDF) if $f(N^[v])ge 1$ and $f(N^+[v])ge 1$ for eachvertex $vin V$. The twin minus domination number of $D$ is$gamma_{}^*(D)=min{w(f)mid f mbox{ is a TMDF of } D}$. Inthis paper, we initiate the study of twin minus domination numbersin digraphs and present some lower bounds for $gamma_{}^*(D)$ interms of the order, size and maximum and minimum indegrees andoutdegrees.
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149
164


Maryam
Atapour
Department of Mathematics
Faculty of basic sciences
University of Bonab
Bonab, Iran, Po. Box: 5551761167
Department of Mathematics
Faculty of basic
Iran
m.atapour@bonabu.ac.ir


Abdollah
Khodkar
Department of Mathematics
University of West Georgia
Carrollton, GA 30118, USA
Department of Mathematics
University of West
United States
akhodkar@westga.edu
twin domination in digraphs
minus domination in graphs
twin minus domination in digraphs
Signed total Roman kdomination in directed graphs
2
2
Let $D$ be a finite and simple digraph with vertex set $V(D)$.A signed total Roman $k$dominating function (STR$k$DF) on$D$ is a function $f:V(D)rightarrow{1, 1, 2}$ satisfying the conditionsthat (i) $sum_{xin N^{}(v)}f(x)ge k$ for each$vin V(D)$, where $N^{}(v)$ consists of all vertices of $D$ fromwhich arcs go into $v$, and (ii) every vertex $u$ for which$f(u)=1$ has an inner neighbor $v$ for which $f(v)=2$.The weight of an STR$k$DF $f$ is $omega(f)=sum_{vin V (D)}f(v)$.The signed total Roman $k$domination number $gamma^{k}_{stR}(D)$of $D$ is the minimum weight of an STR$k$DF on $D$. In this paper weinitiate the study of the signed total Roman $k$domination numberof digraphs, and we present different bounds on $gamma^{k}_{stR}(D)$.In addition, we determine the signed total Roman $k$dominationnumber of some classes of digraphs. Some of our results are extensionsof known properties of the signed total Roman $k$dominationnumber $gamma^{k}_{stR}(G)$ of graphs $G$.
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165
178


Nasrin
Dehgardi
Sirjan University of Technology, Sirjan 78137, Iran
Sirjan University of Technology, Sirjan 78137,
Iran
ndehgardi@gmail.com


Lutz
Volkmann
Lehrstuhl II fur Mathematik,
RWTH Aachen University,
52056 Aachen, Germany
Lehrstuhl II fur Mathematik,
RWTH Aachen
Germany
volkm@math2.rwthaachen.de
Digraph
Signed total Roman kdominating function
Signed total Roman kdomination