eng Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 2538-2136 2017-09-01 2 2 65 85 10.22049/cco.2017.25865.1051 13631 Primal-dual path-following algorithms for circular programming Baha Alzalg baha2math@gmail.com 1 Mohammad Pirhaji mojtabapirhaji@yahoo.com 2 The University of Jordan Shahrekord University 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. http://comb-opt.azaruniv.ac.ir/article_13631_3b92d66c63867691344b503a2f0746f7.pdf Circular cone programming Interior point methods Euclidean Jordan algebra Self-concordance eng Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 2538-2136 2017-09-01 2 2 87 98 10.22049/cco.2017.13630 13630 Reformulated F-index of graph operations Hamideh Aram hamideh.aram@gmail.com 1 Nasrin Dehgardi ndehgardi@gmail.com 2 Department of Mathematics Gareziaeddin Center, Khoy Branch, Islamic Azad University, Khoy, Iran Department of Mathematics and Computer Science, Sirjan University of Technology Sirjan, I.R. Iran 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. http://comb-opt.azaruniv.ac.ir/article_13630_719b7afc30e723e9cbae02669009d3c6.pdf First general Zagreb index reformulated first general Zagreb index F-index reformulated F-index eng Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 2538-2136 2017-09-01 2 2 99 117 10.22049/cco.2017.25949.1059 13643 On leap Zagreb indices of graphs Ivan Gutman gutman@kg.ac.rs 1 Ahmed Naji ama.mohsen78@gmail.com 2 Nandappa Soner ndsoner@yahoo.co.in 3 University of Kragujevac Department of Mathematics, University of Mysore, Mysusu, India Department of Mathematics, University of Mysore, Mysuru, India 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. http://comb-opt.azaruniv.ac.ir/article_13643_fc88ed6fdf52b7f7a7ad4b621f695992.pdf degree (of vertex) Second degree Zagreb indices Leap Zagreb indices eng Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 2538-2136 2017-09-01 2 2 119 138 10.22049/cco.2017.25908.1053 13644 Some results on the complement of a new graph associated to a commutative ring S. Visweswaran s_visweswaran2006@yahoo.co.in 1 Anirudhdha Parmar anirudh.maths@gmail.com 2 Saurashtra University Saurashtra University 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. http://comb-opt.azaruniv.ac.ir/article_13644_1b27eaa14546119e0ee5915425b1cb0b.pdf Annihilating ideal of a ring maximal N-prime of (0) connected graph diameter. girth eng Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 2538-2136 2017-09-01 2 2 139 147 10.22049/cco.2017.25850.1047 13645 Approximation Solutions for Time-Varying Shortest Path Problem Gholam Hassan Shirdel shirdel81math@gmail.com 1 Hassan Rezapour hassan.rezapour@gmail.com 2 University of Qom Unuversity of Qom 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}. http://comb-opt.azaruniv.ac.ir/article_13645_0d39e0bfe8ae0a66991a25e4ac1ac564.pdf Time-Varying Optimization Approximation solutions Shortest Path Problem eng Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 2538-2136 2017-09-01 2 2 149 159 10.22049/cco.2017.25918.1055 13646 Graceful labelings of the generalized Petersen graphs Aleksander Vesel veselfnm@gmail.com 1 Zehui Shao zshao@gzhu.edu.cn 2 Fei Deng dengfei@cdut.cn 3 Zepeng Li lizepeng@pku.edu.cn 4 University of Maribor School of Information Science &amp; Technology, Chengdu University, Chengdu, China College of Information Science and Technology, Chengdu University of Technology, Chengdu, China Key Laboratory of High Confidence Software Technologies, Peking University, Peking, China 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. http://comb-opt.azaruniv.ac.ir/article_13646_07d33d001066dc9b0e695120e6125c8a.pdf graceful labeling generalized Petersen graph heuristic