Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
1
2
2016
12
01
A full Nesterov-Todd step interior-point method for circular cone optimization
83
102
EN
Behrouz
Kheirfam
Azarbaijan Shahid Madani University
b.kheirfam@azaruniv.edu
10.22049/cco.2016.13554
In this paper, we present a full Newton step feasible interior-pointmethod for circular cone optimization by using Euclidean Jordanalgebra. The search direction is based on the Nesterov-Todd scalingscheme, and only full-Newton step is used at each iteration.Furthermore, we derive the iteration bound that coincides with thecurrently best known iteration bound for small-update methods.
Circular cone optimization,Full-Newton step,Interior-point methods,Euclidean Jordan algebra
http://comb-opt.azaruniv.ac.ir/article_13554.html
http://comb-opt.azaruniv.ac.ir/article_13554_9900ae75931b4aada179ad211a6b3724.pdf
Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
1
2
2016
12
01
Hypo-efficient domination and hypo-unique domination
103
116
EN
Vladimir
Samodivkin
University of Architecture, Civil Еngineering and Geodesy;
Department of Mathematics
vl.samodivkin@gmail.com
10.22049/cco.2016.13553
For a graph $G$ let $gamma (G)$ be its domination number. We define a graph G to be (i) a hypo-efficient 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 hypo-unique domination graph (a hypo-$mathcal{UD}$ graph) if $G$ has at least two minimum dominating sets, but $G-v$ 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 $gamma(G-v) < gamma(G)$ 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.
domination number,efficient domination,unique domination,hypo-property
http://comb-opt.azaruniv.ac.ir/article_13553.html
http://comb-opt.azaruniv.ac.ir/article_13553_2afb7e049e6640f7612ba8d81256137c.pdf
Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
1
2
2016
12
01
The sum-annihilating essential ideal graph of a commutative ring
117
135
EN
Abbas
Alilou
Azarbaijan Shahid Madani University
a_alilou@azaruniv.edu
Jafar
Amjadi
Azarbaijan Shahid Madani University
j-amjadi@azaruniv.edu
10.22049/cco.2016.13555
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 non-zero intersectionwith every other non-zero ideal of $R$. Thesum-annihilating essential ideal graph of $R$, denoted by $mathcal{AE}_R$, isa graph whose vertex set is the set of all non-zero 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 sum-annihilating essential ideal graph. We first characterize all rings whose sum-annihilating 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 sum-annihilating essential ideal graph has genus zero or one.
Commutative rings,annihilating ideal,essential ideal,genus of a graph
http://comb-opt.azaruniv.ac.ir/article_13555.html
http://comb-opt.azaruniv.ac.ir/article_13555_3f74eb186e2bee9fefcb8aa541b1f23c.pdf
Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
1
2
2016
12
01
On trees and the multiplicative sum Zagreb index
137
148
EN
Mehdi
Eliasi
Dept. of Mathematics, Khansar Faculty of Mathematics and Computer Science,
Khansar, Iran,
m.elyasi@khansar-cmc.ac.ir
Ali
Ghalavand
Dept. of Mathematics, Khansar Faculty of Mathematics and Computer Science,
Khansar, Iran
ali797ghalavand@gmail.com
10.22049/cco.2016.13574
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 $ngeq 13$.
Multiplicative Sum Zagreb Index,Graph Transformation,Branching Point,trees
http://comb-opt.azaruniv.ac.ir/article_13574.html
http://comb-opt.azaruniv.ac.ir/article_13574_13979e274d477e710da9e35a059bc605.pdf
Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
1
2
2016
12
26
Twin minus domination in directed graphs
149
164
EN
Maryam
Atapour
Department of Mathematics
Faculty of basic sciences
University of Bonab
Bonab, Iran, Po. Box: 5551761167
m.atapour@bonabu.ac.ir
Abdollah
Khodkar
Department of Mathematics
University of West Georgia
Carrollton, GA 30118, USA
akhodkar@westga.edu
10.22049/cco.2016.13575
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 in-degrees andout-degrees.
twin domination in digraphs,minus domination in graphs,twin minus domination in digraphs
http://comb-opt.azaruniv.ac.ir/article_13575.html
http://comb-opt.azaruniv.ac.ir/article_13575_b0af46e588dfc0fa0951f816023dd6df.pdf
Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
1
2
2016
12
30
Signed total Roman k-domination in directed graphs
165
178
EN
Nasrin
Dehgardi
Sirjan University of Technology, Sirjan 78137, Iran
ndehgardi@gmail.com
Lutz
Volkmann
Lehrstuhl II fur Mathematik,
RWTH Aachen University,
52056 Aachen, Germany
volkm@math2.rwth-aachen.de
10.22049/cco.2016.13576
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 $G$.
Digraph,Signed total Roman k-dominating function,Signed total Roman k-domination
http://comb-opt.azaruniv.ac.ir/article_13576.html
http://comb-opt.azaruniv.ac.ir/article_13576_afdcd0fac389c7cc1b729f716dbbce32.pdf