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, <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.
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-<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}.
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 & 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 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.
http://comb-opt.azaruniv.ac.ir/article_13646_07d33d001066dc9b0e695120e6125c8a.pdf
graceful labeling
generalized Petersen graph
heuristic