eng
Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
2016-12-01
1
2
83
102
10.22049/cco.2016.13554
13554
A full Nesterov-Todd step interior-point method for circular cone optimization
Behrouz Kheirfam
b.kheirfam@azaruniv.edu
1
Azarbaijan Shahid Madani University
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.
http://comb-opt.azaruniv.ac.ir/article_13554_9900ae75931b4aada179ad211a6b3724.pdf
Circular cone optimization
Full-Newton step
Interior-point methods
Euclidean Jordan algebra
eng
Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
2016-12-01
1
2
103
116
10.22049/cco.2016.13553
13553
Hypo-efficient domination and hypo-unique domination
Vladimir Samodivkin
vl.samodivkin@gmail.com
1
University of Architecture, Civil Еngineering and Geodesy; Department of Mathematics
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.
http://comb-opt.azaruniv.ac.ir/article_13553_2afb7e049e6640f7612ba8d81256137c.pdf
domination number
efficient domination
unique domination
hypo-property
eng
Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
2016-12-01
1
2
117
135
10.22049/cco.2016.13555
13555
The sum-annihilating essential ideal graph of a commutative ring
Abbas Alilou
a_alilou@azaruniv.edu
1
Jafar Amjadi
j-amjadi@azaruniv.edu
2
Azarbaijan Shahid Madani University
Azarbaijan Shahid Madani University
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.
http://comb-opt.azaruniv.ac.ir/article_13555_3f74eb186e2bee9fefcb8aa541b1f23c.pdf
Commutative rings
annihilating ideal
essential ideal
genus of a graph
eng
Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
2016-12-01
1
2
137
148
10.22049/cco.2016.13574
13574
On trees and the multiplicative sum Zagreb index
Mehdi Eliasi
m.elyasi@khansar-cmc.ac.ir
1
Ali Ghalavand
ali797ghalavand@gmail.com
2
Dept. of Mathematics, Khansar Faculty of Mathematics and Computer Science, Khansar, Iran,
Dept. of Mathematics, Khansar Faculty of Mathematics and Computer Science, Khansar, Iran
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 $ngeq 13$.
http://comb-opt.azaruniv.ac.ir/article_13574_13979e274d477e710da9e35a059bc605.pdf
Multiplicative Sum Zagreb Index
Graph Transformation
Branching Point
trees
eng
Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
2016-12-26
1
2
149
164
10.22049/cco.2016.13575
13575
Twin minus domination in directed graphs
Maryam Atapour
m.atapour@bonabu.ac.ir
1
Abdollah Khodkar
akhodkar@westga.edu
2
Department of Mathematics Faculty of basic sciences University of Bonab Bonab, Iran, Po. Box: 5551761167
Department of Mathematics University of West Georgia Carrollton, GA 30118, USA
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.
http://comb-opt.azaruniv.ac.ir/article_13575_b0af46e588dfc0fa0951f816023dd6df.pdf
twin domination in digraphs
minus domination in graphs
twin minus domination in digraphs
eng
Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
2016-12-30
1
2
165
178
10.22049/cco.2016.13576
13576
Signed total Roman k-domination in directed graphs
Nasrin Dehgardi
ndehgardi@gmail.com
1
Lutz Volkmann
volkm@math2.rwth-aachen.de
2
Sirjan University of Technology, Sirjan 78137, Iran
Lehrstuhl II fur Mathematik, RWTH Aachen University, 52056 Aachen, Germany
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 $G$.
http://comb-opt.azaruniv.ac.ir/article_13576_afdcd0fac389c7cc1b729f716dbbce32.pdf
Digraph
Signed total Roman k-dominating function
Signed total Roman k-domination