Primal-dual path-following algorithms for circular programming
Baha
Alzalg
The University of Jordan
author
Mohammad
Pirhaji
Shahrekord University
author
text
article
2017
eng
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.
Communications in Combinatorics and Optimization
Azarbaijan Shahid Madani University
2538-2128
2
v.
2
no.
2017
65
85
http://comb-opt.azaruniv.ac.ir/article_13631_3b92d66c63867691344b503a2f0746f7.pdf
dx.doi.org/10.22049/cco.2017.25865.1051
Reformulated F-index of graph operations
Hamideh
Aram
Department of Mathematics
Gareziaeddin Center, Khoy Branch, Islamic Azad University, Khoy, Iran
author
Nasrin
Dehgardi
Department of Mathematics and Computer Science,
Sirjan University of Technology
Sirjan, I.R. Iran
author
text
article
2017
eng
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.
Communications in Combinatorics and Optimization
Azarbaijan Shahid Madani University
2538-2128
2
v.
2
no.
2017
87
98
http://comb-opt.azaruniv.ac.ir/article_13630_719b7afc30e723e9cbae02669009d3c6.pdf
dx.doi.org/10.22049/cco.2017.13630
On leap Zagreb indices of graphs
Ivan
Gutman
University of Kragujevac
author
Ahmed
Naji
Department of Mathematics, University of Mysore, Mysusu, India
author
Nandappa
Soner
Department of Mathematics, University of Mysore, Mysuru, India
author
text
article
2017
eng
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.
Communications in Combinatorics and Optimization
Azarbaijan Shahid Madani University
2538-2128
2
v.
2
no.
2017
99
117
http://comb-opt.azaruniv.ac.ir/article_13643_fc88ed6fdf52b7f7a7ad4b621f695992.pdf
dx.doi.org/10.22049/cco.2017.25949.1059
Some results on the complement of a new graph associated to a commutative ring
S.
Visweswaran
Saurashtra University
author
Anirudhdha
Parmar
Saurashtra University
author
text
article
2017
eng
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.
Communications in Combinatorics and Optimization
Azarbaijan Shahid Madani University
2538-2128
2
v.
2
no.
2017
119
138
http://comb-opt.azaruniv.ac.ir/article_13644_1b27eaa14546119e0ee5915425b1cb0b.pdf
dx.doi.org/10.22049/cco.2017.25908.1053
Approximation Solutions for Time-Varying Shortest Path Problem
Gholam Hassan
Shirdel
University of Qom
author
Hassan
Rezapour
Unuversity of Qom
author
text
article
2017
eng
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}.
Communications in Combinatorics and Optimization
Azarbaijan Shahid Madani University
2538-2128
2
v.
2
no.
2017
139
147
http://comb-opt.azaruniv.ac.ir/article_13645_0d39e0bfe8ae0a66991a25e4ac1ac564.pdf
dx.doi.org/10.22049/cco.2017.25850.1047
Graceful labelings of the generalized Petersen graphs
Aleksander
Vesel
University of Maribor
author
Zehui
Shao
School of Information Science & Technology, Chengdu University, Chengdu, China
author
Fei
Deng
College of Information Science and Technology, Chengdu University of Technology, Chengdu, China
author
Zepeng
Li
Key Laboratory of High Confidence Software Technologies, Peking University, Peking, China
author
text
article
2017
eng
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.
Communications in Combinatorics and Optimization
Azarbaijan Shahid Madani University
2538-2128
2
v.
2
no.
2017
149
159
http://comb-opt.azaruniv.ac.ir/article_13646_07d33d001066dc9b0e695120e6125c8a.pdf
dx.doi.org/10.22049/cco.2017.25918.1055