Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 2538-2136 2 2 2017 09 01 Primal-dual path-following algorithms for circular programming 65 85 EN Baha Alzalg The University of Jordan baha2math@gmail.com Mohammad Pirhaji Shahrekord University mojtabapirhaji@yahoo.com 10.22049/cco.2017.25865.1051 Circular programming problems are a new class of convex optimization problems that include second-order cone programming problems as a special case. Alizadeh and Goldfarb [Math. Program. Ser. A 95 (2003) 3-51] introduced primal-dual path-following algorithms for solving second-order cone programming problems. In this paper, we generalize their work by using the machinery of Euclidean Jordan algebras associated with the circular cones to derive primal-dual path-following interior point algorithms for circular programming problems. We prove polynomial convergence of the proposed algorithms by showing that the circular logarithmic barrier is a strongly self-concordant barrier. The numerical examples show the path-following algorithms are simple and efficient. Circular cone programming,Interior point methods,Euclidean Jordan algebra,Self-concordance http://comb-opt.azaruniv.ac.ir/article_13631.html http://comb-opt.azaruniv.ac.ir/article_13631_3b92d66c63867691344b503a2f0746f7.pdf
Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 2538-2136 2 2 2017 09 01 Reformulated F-index of graph operations 87 98 EN Hamideh Aram Department of Mathematics Gareziaeddin Center, Khoy Branch, Islamic Azad University, Khoy, Iran hamideh.aram@gmail.com Nasrin Dehgardi Department of Mathematics and Computer Science, Sirjan University of Technology Sirjan, I.R. Iran ndehgardi@gmail.com 10.22049/cco.2017.13630 The first general Zagreb index is defined as \$M_1^lambda(G)=sum_{vin V(G)}d_{G}(v)^lambda\$. The case \$lambda=3\$, is called F-index. Similarly, reformulated first general Zagreb index is defined in terms of edge-drees as \$EM_1^lambda(G)=sum_{ein E(G)}d_{G}(e)^lambda\$ and the reformulated F-index is \$RF(G)=sum_{ein E(G)}d_{G}(e)^3\$. In this paper, we compute the reformulated F-index for some graph operations. First general Zagreb index,reformulated first general Zagreb index,F-index,reformulated F-index http://comb-opt.azaruniv.ac.ir/article_13630.html http://comb-opt.azaruniv.ac.ir/article_13630_719b7afc30e723e9cbae02669009d3c6.pdf
Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 2538-2136 2 2 2017 09 01 On leap Zagreb indices of graphs 99 117 EN Ivan Gutman University of Kragujevac gutman@kg.ac.rs Ahmed M Naji 0000-0003-0007-8927 Department of Mathematics, University of Mysore, Mysusu, India ama.mohsen78@gmail.com Nandappa D Soner Department of Mathematics, University of Mysore, Mysuru, India ndsoner@yahoo.co.in 10.22049/cco.2017.25949.1059 The first and second Zagreb indices of a graph are equal, <br />respectively, to the sum of squares of the vertex degrees, <br />and the sum of the products of the degrees of pairs of <br />adjacent vertices. We now consider analogous graph <br />invariants, based on the second degrees of vertices <br />(number of their second neighbors), called leap Zagreb <br />indices. A number of their basic properties is established. degree (of vertex),Second degree,Zagreb indices,leap Zagreb indices http://comb-opt.azaruniv.ac.ir/article_13643.html http://comb-opt.azaruniv.ac.ir/article_13643_fc88ed6fdf52b7f7a7ad4b621f695992.pdf
Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 2538-2136 2 2 2017 09 01 Some results on the complement of a new graph associated to a commutative ring 119 138 EN S. Visweswaran Saurashtra University s_visweswaran2006@yahoo.co.in Anirudhdha Parmar Saurashtra University anirudh.maths@gmail.com 10.22049/cco.2017.25908.1053 The rings considered in this article are commutative with identity which are not fields. Let R be a ring. A. Alilou, J. Amjadi and Sheikholeslami introduced and investigated a graph whose vertex set is the set of all nontrivial ideals of R and distinct vertices I, J are joined by an edge in this graph if and only if either ann(I)J = (0) or ann(J)I = (0). They called this graph as a new graph associated to a commutative ring.Their above mentioned work appeared in the Journal, Discrete Mathematics Algorithms and Applications. The aim of this article is to investigate the interplay between some graph- theoretic properties of the complement of a new graph associated to a commutative ring R and the ring -theoretic-properties of R. Annihilating ideal of a ring,maximal N-prime of (0),connected graph,diameter. girth http://comb-opt.azaruniv.ac.ir/article_13644.html http://comb-opt.azaruniv.ac.ir/article_13644_1b27eaa14546119e0ee5915425b1cb0b.pdf
Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 2538-2136 2 2 2017 09 01 Approximation Solutions for Time-Varying Shortest Path Problem 139 147 EN Gholam Hassan Shirdel 0000000327594606 University of Qom shirdel81math@gmail.com Hassan Rezapour Unuversity of Qom hassan.rezapour@gmail.com 10.22049/cco.2017.25850.1047 Abstract. Time-varying network optimization problems have tradition-<br />ally been solved by specialized algorithms. These algorithms have NP-<br />complement time complexity. This paper considers the time-varying short-<br />est path problem, in which can be optimally solved in O(T(m + n)) time,<br />where T is a given integer. For this problem with arbitrary waiting times,<br />we propose an approximation algorithm, which can solve the problem with<br />O(T(m+n)/ k ) time complexity such that evaluates only a subset of the values<br />for t = {0, 1, . . . , T}. Time-Varying Optimization,Approximation solutions,Shortest Path Problem http://comb-opt.azaruniv.ac.ir/article_13645.html http://comb-opt.azaruniv.ac.ir/article_13645_0d39e0bfe8ae0a66991a25e4ac1ac564.pdf
Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 2538-2136 2 2 2017 09 01 Graceful labelings of the generalized Petersen graphs 149 159 EN Aleksander Vesel University of Maribor veselfnm@gmail.com Zehui Shao School of Information Science &amp; Technology, Chengdu University, Chengdu, China zshao@gzhu.edu.cn Fei Deng College of Information Science and Technology, Chengdu University of Technology, Chengdu, China dengfei@cdut.cn Zepeng Li Key Laboratory of High Confidence Software Technologies, Peking University, Peking, China lizepeng@pku.edu.cn 10.22049/cco.2017.25918.1055 A graceful labeling of a graph \$G=(V,E)\$ with \$m\$ edges is an<br />injection \$f: V(G) rightarrow {0,1,ldots,m}\$ such that the resulting edge labels<br />obtained by \$|f(u)-f(v)|\$ on every edge \$uv\$ are pairwise distinct.<br /> For natural numbers \$n\$ and \$k\$, where \$n > 2k\$, a generalized Petersen<br />graph \$P(n, k)\$ is the graph whose vertex set is \${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}\$ and its edge set is \${u_iu_{i+1}, u_iv_i, v_iv_{i+k} : 1 leq i leq n }\$, where subscript arithmetic is done modulo \$n\$. <br />We propose a backtracking algorithm with a specific static variable ordering and dynamic value ordering to find graceful labelings for generalized Petersen graphs.<br />Experimental results show that the presented approach strongly outperforms the standard backtracking algorithm. The proposed algorithm is able to find graceful labelings for all <br />generalized Petersen graphs \$P(n, k)\$ with \$n le 75\$ within only several seconds. graceful labeling,generalized Petersen graph,heuristic http://comb-opt.azaruniv.ac.ir/article_13646.html http://comb-opt.azaruniv.ac.ir/article_13646_07d33d001066dc9b0e695120e6125c8a.pdf