ORIGINAL_ARTICLE
Primal-dual path-following algorithms for circular programming
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
2017-09-01T11:23:20
2020-08-11T11:23:20
65
85
10.22049/cco.2017.25865.1051
Circular cone programming
Interior point methods
Euclidean Jordan algebra
Self-concordance
Baha
Alzalg
baha2math@gmail.com
true
1
The University of Jordan
The University of Jordan
The University of Jordan
LEAD_AUTHOR
Mohammad
Pirhaji
mojtabapirhaji@yahoo.com
true
2
Shahrekord University
Shahrekord University
Shahrekord University
AUTHOR
ORIGINAL_ARTICLE
Reformulated F-index of graph operations
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
2017-09-01T11:23:20
2020-08-11T11:23:20
87
98
10.22049/cco.2017.13630
First general Zagreb index
reformulated first general Zagreb index
F-index
reformulated F-index
Hamideh
Aram
hamideh.aram@gmail.com
true
1
Department of Mathematics
Gareziaeddin Center, Khoy Branch, Islamic Azad University, Khoy, Iran
Department of Mathematics
Gareziaeddin Center, Khoy Branch, Islamic Azad University, Khoy, Iran
Department of Mathematics
Gareziaeddin Center, Khoy Branch, Islamic Azad University, Khoy, Iran
LEAD_AUTHOR
Nasrin
Dehgardi
ndehgardi@gmail.com
true
2
Department of Mathematics and Computer Science,
Sirjan University of Technology
Sirjan, I.R. Iran
Department of Mathematics and Computer Science,
Sirjan University of Technology
Sirjan, I.R. Iran
Department of Mathematics and Computer Science,
Sirjan University of Technology
Sirjan, I.R. Iran
AUTHOR
ORIGINAL_ARTICLE
On leap Zagreb indices of graphs
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
2017-09-01T11:23:20
2020-08-11T11:23:20
99
117
10.22049/cco.2017.25949.1059
degree (of vertex)
Second degree
Zagreb indices
leap Zagreb indices
Ivan
Gutman
gutman@kg.ac.rs
true
1
University of Kragujevac
University of Kragujevac
University of Kragujevac
LEAD_AUTHOR
Ahmed
Naji
ama.mohsen78@gmail.com
true
2
Department of Mathematics, University of Mysore, Mysusu, India
Department of Mathematics, University of Mysore, Mysusu, India
Department of Mathematics, University of Mysore, Mysusu, India
AUTHOR
Nandappa
Soner
ndsoner@yahoo.co.in
true
3
Department of Mathematics, University of Mysore, Mysuru, India
Department of Mathematics, University of Mysore, Mysuru, India
Department of Mathematics, University of Mysore, Mysuru, India
AUTHOR
ORIGINAL_ARTICLE
Some results on the complement of a new graph associated to a commutative ring
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
2017-09-01T11:23:20
2020-08-11T11:23:20
119
138
10.22049/cco.2017.25908.1053
Annihilating ideal of a ring
maximal N-prime of (0)
connected graph
diameter. girth
S.
Visweswaran
s_visweswaran2006@yahoo.co.in
true
1
Saurashtra University
Saurashtra University
Saurashtra University
LEAD_AUTHOR
Anirudhdha
Parmar
anirudh.maths@gmail.com
true
2
Saurashtra University
Saurashtra University
Saurashtra University
AUTHOR
ORIGINAL_ARTICLE
Approximation Solutions for Time-Varying Shortest Path Problem
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
2017-09-01T11:23:20
2020-08-11T11:23:20
139
147
10.22049/cco.2017.25850.1047
Time-Varying Optimization
Approximation solutions
Shortest Path Problem
Gholam Hassan
Shirdel
shirdel81math@gmail.com
true
1
University of Qom
University of Qom
University of Qom
LEAD_AUTHOR
Hassan
Rezapour
hassan.rezapour@gmail.com
true
2
Unuversity of Qom
Unuversity of Qom
Unuversity of Qom
AUTHOR
ORIGINAL_ARTICLE
Graceful labelings of the generalized Petersen graphs
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
2017-09-01T11:23:20
2020-08-11T11:23:20
149
159
10.22049/cco.2017.25918.1055
graceful labeling
generalized Petersen graph
heuristic
Aleksander
Vesel
veselfnm@gmail.com
true
1
University of Maribor
University of Maribor
University of Maribor
LEAD_AUTHOR
Zehui
Shao
zshao@gzhu.edu.cn
true
2
School of Information Science & Technology, Chengdu University, Chengdu, China
School of Information Science & Technology, Chengdu University, Chengdu, China
School of Information Science & Technology, Chengdu University, Chengdu, China
AUTHOR
Fei
Deng
dengfei@cdut.cn
true
3
College of Information Science and Technology, Chengdu University of Technology, Chengdu, China
College of Information Science and Technology, Chengdu University of Technology, Chengdu, China
College of Information Science and Technology, Chengdu University of Technology, Chengdu, China
AUTHOR
Zepeng
Li
lizepeng@pku.edu.cn
true
4
Key Laboratory of High Confidence Software Technologies, Peking University, Peking, China
Key Laboratory of High Confidence Software Technologies, Peking University, Peking, China
Key Laboratory of High Confidence Software Technologies, Peking University, Peking, China
AUTHOR