Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21281220161201A full Nesterov-Todd step interior-point method for circular cone optimization831021355410.22049/cco.2016.13554ENBehrouzKheirfamAzarbaijan Shahid Madani UniversityJournal Article20160103In 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.Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21281220161201Hypo-efficient domination and hypo-unique domination1031161355310.22049/cco.2016.13553ENVladimirSamodivkinUniversity of Architecture, Civil Еngineering and Geodesy;
Department of Mathematics0000-0001-7934-5789Journal Article20160111For 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.Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21281220161201The sum-annihilating essential ideal graph of a commutative ring1171351355510.22049/cco.2016.13555ENAbbasAlilouAzarbaijan Shahid Madani UniversityJafarAmjadiAzarbaijan Shahid Madani University0000-0001-9340-4773Journal Article20160310Let $R$ 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.Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21281220161201On trees and the multiplicative sum Zagreb index1371481357410.22049/cco.2016.13574ENMehdiEliasiDept. of Mathematics, Khansar Faculty of Mathematics and Computer Science,
Khansar, Iran,AliGhalavandDept. of Mathematics, Khansar Faculty of Mathematics and Computer Science,
Khansar, IranJournal Article20160928For 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 $ngeq 13$.Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21281220161226Twin minus domination in directed graphs1491641357510.22049/cco.2016.13575ENMaryamAtapourDepartment of Mathematics
Faculty of basic sciences
University of Bonab
Bonab, Iran, Po. Box: 5551761167AbdollahKhodkarDepartment of Mathematics
University of West Georgia
Carrollton, GA 30118, USAJournal Article20160209Let $D=(V,A)$ 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.Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21281220161230Signed total Roman k-domination in directed graphs1651781357610.22049/cco.2016.13576ENNasrinDehgardiSirjan University of Technology, Sirjan 78137, IranLutzVolkmannLehrstuhl II fur Mathematik,
RWTH Aachen University,
52056 Aachen, Germany0000-0003-3496-277XJournal Article20160913Let $D$ 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 $G$.