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 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, respectively, to the sum of squares of the vertex degrees, and the sum of the products of the degrees of pairs of adjacent vertices. We now consider analogous graph invariants, based on the second degrees of vertices (number of their second neighbors), called leap Zagreb 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 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-ally been solved by specialized algorithms. These algorithms have NP-complement time complexity. This paper considers the time-varying short-est path problem, in which can be optimally solved in O(T(m + n)) time,where T is a given integer. For this problem with arbitrary waiting times,we propose an approximation algorithm, which can solve the problem withO(T(m+n)/ k ) time complexity such that evaluates only a subset of the valuesfor 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 aninjection \$f: V(G) rightarrow {0,1,ldots,m}\$ such that the resulting edge labelsobtained by \$|f(u)-f(v)|\$ on every edge \$uv\$ are pairwise distinct. For natural numbers \$n\$ and \$k\$, where \$n > 2k\$, a generalized Petersengraph \$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\$. We propose a backtracking algorithm with a specific static variable ordering and dynamic value ordering to find graceful labelings for generalized Petersen graphs.Experimental results show that the presented approach strongly outperforms the standard backtracking algorithm. The proposed algorithm is able to find graceful labelings for all 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