Commun. Comb. Optim. Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Azarbaijan Shahid Madani University 90 10.22049/cco.2016.13554 Operations research, mathematical programming A full Nesterov-Todd step interior-point method for circular cone optimization A full Nesterov-Todd step interior-point method for circular cone optimization Kheirfam Behrouz Azarbaijan Shahid Madani University 01 12 2016 1 2 83 102 03 01 2016 16 09 2016 Copyright © 2016, Azarbaijan Shahid Madani University. 2016 http://comb-opt.azaruniv.ac.ir/article_13554.html

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
Commun. Comb. Optim. Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Azarbaijan Shahid Madani University 90 10.22049/cco.2016.13553 Graph theory Hypo-efficient domination and hypo-unique domination Hypo-efficient domination and hypo-unique domination Samodivkin Vladimir University of Architecture, Civil Еngineering and Geodesy; Department of Mathematics 01 12 2016 1 2 103 116 11 01 2016 14 09 2016 Copyright © 2016, Azarbaijan Shahid Madani University. 2016 http://comb-opt.azaruniv.ac.ir/article_13553.html

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
Commun. Comb. Optim. Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Azarbaijan Shahid Madani University 90 10.22049/cco.2016.13555 Algebraic combinatorics The sum-annihilating essential ideal graph of a commutative ring The sum-annihilating essential ideal graph of a commutative ring Alilou Abbas Azarbaijan Shahid Madani University Amjadi Jafar Azarbaijan Shahid Madani University 01 12 2016 1 2 117 135 10 03 2016 29 09 2016 Copyright © 2016, Azarbaijan Shahid Madani University. 2016 http://comb-opt.azaruniv.ac.ir/article_13555.html

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
Commun. Comb. Optim. Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Azarbaijan Shahid Madani University 90 10.22049/cco.2016.13574 Graph theory On trees and the multiplicative sum Zagreb index On trees and the multiplicative sum Zagreb index Eliasi Mehdi Dept. of Mathematics, Khansar Faculty of Mathematics and Computer Science, Khansar, Iran, Ghalavand Ali Dept. of Mathematics, Khansar Faculty of Mathematics and Computer Science, Khansar, Iran 01 12 2016 1 2 137 148 28 09 2016 24 12 2016 Copyright © 2016, Azarbaijan Shahid Madani University. 2016 http://comb-opt.azaruniv.ac.ir/article_13574.html

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
Commun. Comb. Optim. Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Azarbaijan Shahid Madani University 90 10.22049/cco.2016.13575 Graph theory Twin minus domination in directed graphs Twin minus domination in directed graphs Atapour Maryam Department of Mathematics Faculty of basic sciences University of Bonab Bonab, Iran, Po. Box: 5551761167 Khodkar Abdollah Department of Mathematics University of West Georgia Carrollton, GA 30118, USA 26 12 2016 1 2 149 164 09 02 2016 26 12 2016 Copyright © 2016, Azarbaijan Shahid Madani University. 2016 http://comb-opt.azaruniv.ac.ir/article_13575.html

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
Commun. Comb. Optim. Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Azarbaijan Shahid Madani University 90 10.22049/cco.2016.13576 Graph theory Signed total Roman k-domination in directed graphs Signed total Roman k-domination in directed graphs Dehgardi Nasrin Sirjan University of Technology, Sirjan 78137, Iran Volkmann Lutz Lehrstuhl II fur Mathematik, RWTH Aachen University, 52056 Aachen, Germany 30 12 2016 1 2 165 178 13 09 2016 26 12 2016 Copyright © 2016, Azarbaijan Shahid Madani University. 2016 http://comb-opt.azaruniv.ac.ir/article_13576.html

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