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 method for circular cone optimization by using Euclidean Jordan algebra. The search direction is based on the Nesterov-Todd scaling scheme, and only full-Newton step is used at each iteration. Furthermore, we derive the iteration bound that coincides with the currently best known iteration bound for small-update methods.https://comb-opt.azaruniv.ac.ir/article_13554_9900ae75931b4aada179ad211a6b3724.pdfAzarbaijan 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 MathematicsJournal Article20160111For 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 $v\in V(G)$. 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. https://comb-opt.azaruniv.ac.ir/article_13553_2afb7e049e6640f7612ba8d81256137c.pdfAzarbaijan 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 UniversityJournal Article20160310Let $R$ be a commutative ring with identity. An ideal $I$ of a ring $R$ is called an annihilating ideal if there exists $r\in R\setminus \{0\}$ such that $Ir=(0)$ and an ideal $I$ of $R$ is called an essential ideal if $I$ has non-zero intersection with every other non-zero ideal of $R$. The sum-annihilating essential ideal graph of $R$, denoted by $\mathcal{AE}_R$, is a graph whose vertex set is the set of all non-zero annihilating ideals and two vertices $I$ and $J$ are adjacent whenever ${\rm Ann}(I)+{\rm Ann}(J)$ is an essential ideal. In this paper we initiate the 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. Furthermore determine all isomorphism classes of Artinian rings whose sum-annihilating essential ideal graph has genus zero or one.https://comb-opt.azaruniv.ac.ir/article_13555_3f74eb186e2bee9fefcb8aa541b1f23c.pdfAzarbaijan 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 $\Pi^*(G)=\Pi_{uv\in E(G)}[d_G(u)+d_G(v)]$, where $d_G(v)$ is the degree of vertex $v$ in $G$. In this paper, we first introduce some graph transformations that decrease this index. In application, we identify the fourteen class of trees, with the first through fourteenth smallest multiplicative sum Zagreb indices among all trees of order $n\geq 13$.https://comb-opt.azaruniv.ac.ir/article_13574_13979e274d477e710da9e35a059bc605.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21281220161201Twin 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 $f:V\longrightarrow \{-1,0,1\}$ is called a twin minus dominating function if $f(N^-[v])\ge 1$ and $f(N^+[v])\ge 1$ for each vertex $v\in V$. The twin minus domination number of $D$ is $\gamma_{-}^*(D)=\min\{w(f)\mid f \mbox{ is a twin minus dominating function of } D\}$. In this paper, we initiate the study of twin minus domination numbers in digraphs and present some lower bounds for $\gamma_{-}^*(D)$ in terms of the order, size and maximum and minimum in-degrees and out-degrees.https://comb-opt.azaruniv.ac.ir/article_13575_b0af46e588dfc0fa0951f816023dd6df.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21281220161201Signed 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, GermanyJournal Article20160913Let $D$ 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 conditions that (i) $\sum_{x\in N^{-}(v)}f(x)\ge k$ for each $v\in V(D)$, where $N^{-}(v)$ consists of all vertices of $D$ from which 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 $\omega(f)=\sum_{v\in V (D)}f(v)$. 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 we initiate the study of the signed total Roman $k$-domination number of digraphs, and we present different bounds on $\gamma^{k}_{stR}(D)$. In addition, we determine the signed total Roman $k$-domination number of some classes of digraphs. Some of our results are extensions of known properties of the signed total Roman $k$-domination number $\gamma^{k}_{stR}(G)$ of graphs $G$.https://comb-opt.azaruniv.ac.ir/article_13576_afdcd0fac389c7cc1b729f716dbbce32.pdf