2020-08-05T03:13:50Z
http://comb-opt.azaruniv.ac.ir/?_action=export&rf=summon&issue=2220
Communications in Combinatorics and Optimization
Commun. Comb. Optim.
2538-2128
2538-2128
2016
1
2
A full Nesterov-Todd step interior-point method for circular cone optimization
Behrouz
Kheirfam
In this paper, we present a full Newton step feasible interior-point<br />method for circular cone optimization by using Euclidean Jordan<br />algebra. The search direction is based on the Nesterov-Todd scaling<br />scheme, and only full-Newton step is used at each iteration.<br />Furthermore, we derive the iteration bound that coincides with the<br />currently best known iteration bound for small-update methods.
Circular cone optimization
Full-Newton step
Interior-point methods
Euclidean Jordan algebra
2016
12
01
83
102
http://comb-opt.azaruniv.ac.ir/article_13554_9900ae75931b4aada179ad211a6b3724.pdf
Communications in Combinatorics and Optimization
Commun. Comb. Optim.
2538-2128
2538-2128
2016
1
2
Hypo-efficient domination and hypo-unique domination
Vladimir
Samodivkin
For a graph $G$ let $gamma (G)$ be its domination number. We define a graph G to be <br />(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
2016
12
01
103
116
http://comb-opt.azaruniv.ac.ir/article_13553_2afb7e049e6640f7612ba8d81256137c.pdf
Communications in Combinatorics and Optimization
Commun. Comb. Optim.
2538-2128
2538-2128
2016
1
2
The sum-annihilating essential ideal graph of a commutative ring
Abbas
Alilou
Jafar
Amjadi
Let $R$ be a commutative ring with identity. An ideal $I$ of a ring $R$<br />is called an annihilating ideal if there exists $rin Rsetminus {0}$ such that $Ir=(0)$ and an ideal $I$ of<br />$R$ is called an essential ideal if $I$ has non-zero intersection<br />with every other non-zero ideal of $R$. The<br />sum-annihilating essential ideal graph of $R$, denoted by $mathcal{AE}_R$, is<br />a graph whose vertex set is the set of all non-zero annihilating ideals and two<br />vertices $I$ and $J$ are adjacent whenever ${rm Ann}(I)+{rm<br />Ann}(J)$ is an essential ideal. In this paper we initiate the<br />study 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.<br /> 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
2016
12
01
117
135
http://comb-opt.azaruniv.ac.ir/article_13555_3f74eb186e2bee9fefcb8aa541b1f23c.pdf
Communications in Combinatorics and Optimization
Commun. Comb. Optim.
2538-2128
2538-2128
2016
1
2
On trees and the multiplicative sum Zagreb index
Mehdi
Eliasi
Ali
Ghalavand
For a graph $G$ with edge set $E(G)$, the multiplicative sum Zagreb index of $G$ is defined as<br />$Pi^*(G)=Pi_{uvin E(G)}[d_G(u)+d_G(v)]$, where $d_G(v)$ is the degree of vertex $v$ in $G$.<br />In this paper, we first introduce some graph transformations that decrease<br />this 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
2016
12
01
137
148
http://comb-opt.azaruniv.ac.ir/article_13574_13979e274d477e710da9e35a059bc605.pdf
Communications in Combinatorics and Optimization
Commun. Comb. Optim.
2538-2128
2538-2128
2016
1
2
Twin minus domination in directed graphs
Maryam
Atapour
Abdollah
Khodkar
Let $D=(V,A)$ be a finite simple directed graph. A function<br />$f:Vlongrightarrow {-1,0,1}$ is called a twin minus dominating<br />function (TMDF) if $f(N^-[v])ge 1$ and $f(N^+[v])ge 1$ for each<br />vertex $vin V$. The twin minus domination number of $D$ is<br />$gamma_{-}^*(D)=min{w(f)mid f mbox{ is a TMDF of } D}$. In<br />this paper, we initiate the study of twin minus domination numbers<br />in digraphs and present some lower bounds for $gamma_{-}^*(D)$ in<br />terms of the order, size and maximum and minimum in-degrees and<br />out-degrees.
twin domination in digraphs
minus domination in graphs
twin minus domination in digraphs
2016
12
26
149
164
http://comb-opt.azaruniv.ac.ir/article_13575_b0af46e588dfc0fa0951f816023dd6df.pdf
Communications in Combinatorics and Optimization
Commun. Comb. Optim.
2538-2128
2538-2128
2016
1
2
Signed total Roman k-domination in directed graphs
Nasrin
Dehgardi
Lutz
Volkmann
Let $D$ be a finite and simple digraph with vertex set $V(D)$.<br />A signed total Roman $k$-dominating function (STR$k$DF) on<br />$D$ is a function $f:V(D)rightarrow{-1, 1, 2}$ satisfying the conditions<br />that (i) $sum_{xin N^{-}(v)}f(x)ge k$ for each<br />$vin V(D)$, where $N^{-}(v)$ consists of all vertices of $D$ from<br />which arcs go into $v$, and (ii) every vertex $u$ for which<br />$f(u)=-1$ has an inner neighbor $v$ for which $f(v)=2$.<br />The weight of an STR$k$DF $f$ is $omega(f)=sum_{vin V (D)}f(v)$.<br />The signed total Roman $k$-domination number $gamma^{k}_{stR}(D)$<br />of $D$ is the minimum weight of an STR$k$DF on $D$. In this paper we<br />initiate the study of the signed total Roman $k$-domination number<br />of digraphs, and we present different bounds on $gamma^{k}_{stR}(D)$.<br />In addition, we determine the signed total Roman $k$-domination<br />number of some classes of digraphs. Some of our results are extensions<br />of known properties of the signed total Roman $k$-domination<br />number $gamma^{k}_{stR}(G)$ of graphs $G$.
Digraph
Signed total Roman k-dominating function
Signed total Roman k-domination
2016
12
30
165
178
http://comb-opt.azaruniv.ac.ir/article_13576_afdcd0fac389c7cc1b729f716dbbce32.pdf