Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 2 2 2017 09 01 Primal-dual path-following algorithms for circular programming 65 85 13631 10.22049/cco.2017.25865.1051 EN Baha Alzalg The University of Jordan Mohammad Pirhaji Shahrekord University Journal Article 2017 01 23 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.
Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 2 2 2017 09 01 Reformulated F-index of graph operations 87 98 13630 10.22049/cco.2017.13630 EN Hamideh Aram Department of Mathematics Gareziaeddin Center, Khoy Branch, Islamic Azad University, Khoy, Iran Nasrin Dehgardi Department of Mathematics and Computer Science, Sirjan University of Technology Sirjan, I.R. Iran Journal Article 2017 03 18 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.
Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 2 2 2017 09 01 On leap Zagreb indices of graphs 99 117 13643 10.22049/cco.2017.25949.1059 EN Ivan Gutman University of Kragujevac Ahmed M Naji Department of Mathematics, University of Mysore, Mysusu, India 0000-0003-0007-8927 Nandappa D Soner Department of Mathematics, University of Mysore, Mysuru, India Journal Article 2017 05 30 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.
Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 2 2 2017 09 01 Some results on the complement of a new graph associated to a commutative ring 119 138 13644 10.22049/cco.2017.25908.1053 EN S. Visweswaran Saurashtra University Anirudhdha Parmar Saurashtra University Journal Article 2017 03 07 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.
Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 2 2 2017 09 01 Approximation Solutions for Time-Varying Shortest Path Problem 139 147 13645 10.22049/cco.2017.25850.1047 EN Gholam Hassan Shirdel University of Qom 0000000327594606 Hassan Rezapour Unuversity of Qom Journal Article 2017 01 03 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}.
Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 2 2 2017 09 01 Graceful labelings of the generalized Petersen graphs 149 159 13646 10.22049/cco.2017.25918.1055 EN Aleksander Vesel University of Maribor Zehui Shao School of Information Science &amp; Technology, Chengdu University, Chengdu, China Fei Deng College of Information Science and Technology, Chengdu University of Technology, Chengdu, China Zepeng Li Key Laboratory of High Confidence Software Technologies, Peking University, Peking, China Journal Article 2017 03 20 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.