Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21282220170901Primal-dual path-following algorithms for circular programming65851363110.22049/cco.2017.25865.1051ENBahaAlzalgThe University of JordanMohammadPirhajiShahrekord UniversityJournal Article20170123Circular 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 UniversityCommunications in Combinatorics and Optimization2538-21282220170901Reformulated F-index of graph operations87981363010.22049/cco.2017.13630ENHamidehAramDepartment of Mathematics
Gareziaeddin Center, Khoy Branch, Islamic Azad University, Khoy, IranNasrinDehgardiDepartment of Mathematics and Computer Science,
Sirjan University of Technology
Sirjan, I.R. IranJournal Article20170318The 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 UniversityCommunications in Combinatorics and Optimization2538-21282220170901On leap Zagreb indices of graphs991171364310.22049/cco.2017.25949.1059ENIvanGutmanUniversity of KragujevacAhmed MNajiDepartment of Mathematics, University of Mysore, Mysusu, India0000-0003-0007-8927Nandappa DSonerDepartment of Mathematics, University of Mysore, Mysuru, IndiaJournal Article20170530The 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 UniversityCommunications in Combinatorics and Optimization2538-21282220170901Some results on the complement of a new graph associated to a commutative ring1191381364410.22049/cco.2017.25908.1053ENS.VisweswaranSaurashtra UniversityAnirudhdhaParmarSaurashtra UniversityJournal Article20170307The 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 UniversityCommunications in Combinatorics and Optimization2538-21282220170901Approximation Solutions for Time-Varying Shortest Path Problem1391471364510.22049/cco.2017.25850.1047ENGholam HassanShirdelUniversity of Qom0000000327594606HassanRezapourUnuversity of QomJournal Article20170103Abstract. 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 UniversityCommunications in Combinatorics and Optimization2538-21282220170901Graceful labelings of the generalized Petersen graphs1491591364610.22049/cco.2017.25918.1055ENAleksanderVeselUniversity of MariborZehuiShaoSchool of Information Science & Technology, Chengdu University, Chengdu, ChinaFeiDengCollege of Information Science and Technology, Chengdu University of Technology, Chengdu, ChinaZepengLiKey Laboratory of High Confidence Software Technologies, Peking University, Peking, ChinaJournal Article20170320A 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.