Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
2
2
2017
09
01
Primal-dual path-following algorithms for circular programming
65
85
EN
Baha
Alzalg
The University of Jordan
baha2math@gmail.com
Mohammad
Pirhaji
Shahrekord University
mojtabapirhaji@yahoo.com
10.22049/cco.2017.25865.1051
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.
Circular cone programming,Interior point methods,Euclidean Jordan algebra,Self-concordance
http://comb-opt.azaruniv.ac.ir/article_13631.html
http://comb-opt.azaruniv.ac.ir/article_13631_3b92d66c63867691344b503a2f0746f7.pdf
Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
2
2
2017
09
01
Reformulated F-index of graph operations
87
98
EN
Hamideh
Aram
Department of Mathematics
Gareziaeddin Center, Khoy Branch, Islamic Azad University, Khoy, Iran
hamideh.aram@gmail.com
Nasrin
Dehgardi
Department of Mathematics and Computer Science,
Sirjan University of Technology
Sirjan, I.R. Iran
ndehgardi@gmail.com
10.22049/cco.2017.13630
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.
First general Zagreb index,reformulated first general Zagreb index,F-index,reformulated F-index
http://comb-opt.azaruniv.ac.ir/article_13630.html
http://comb-opt.azaruniv.ac.ir/article_13630_719b7afc30e723e9cbae02669009d3c6.pdf
Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
2
2
2017
09
01
On leap Zagreb indices of graphs
99
117
EN
Ivan
Gutman
University of Kragujevac
gutman@kg.ac.rs
Ahmed
M
Naji
0000-0003-0007-8927
Department of Mathematics, University of Mysore, Mysusu, India
ama.mohsen78@gmail.com
Nandappa
D
Soner
Department of Mathematics, University of Mysore, Mysuru, India
ndsoner@yahoo.co.in
10.22049/cco.2017.25949.1059
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.
degree (of vertex),Second degree,Zagreb indices,leap Zagreb indices
http://comb-opt.azaruniv.ac.ir/article_13643.html
http://comb-opt.azaruniv.ac.ir/article_13643_fc88ed6fdf52b7f7a7ad4b621f695992.pdf
Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
2
2
2017
09
01
Some results on the complement of a new graph associated to a commutative ring
119
138
EN
S.
Visweswaran
Saurashtra University
s_visweswaran2006@yahoo.co.in
Anirudhdha
Parmar
Saurashtra University
anirudh.maths@gmail.com
10.22049/cco.2017.25908.1053
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.
Annihilating ideal of a ring,maximal N-prime of (0),connected graph,diameter. girth
http://comb-opt.azaruniv.ac.ir/article_13644.html
http://comb-opt.azaruniv.ac.ir/article_13644_1b27eaa14546119e0ee5915425b1cb0b.pdf
Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
2
2
2017
09
01
Approximation Solutions for Time-Varying Shortest Path Problem
139
147
EN
Gholam Hassan
Shirdel
0000000327594606
University of Qom
shirdel81math@gmail.com
Hassan
Rezapour
Unuversity of Qom
hassan.rezapour@gmail.com
10.22049/cco.2017.25850.1047
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}.
Time-Varying Optimization,Approximation solutions,Shortest Path Problem
http://comb-opt.azaruniv.ac.ir/article_13645.html
http://comb-opt.azaruniv.ac.ir/article_13645_0d39e0bfe8ae0a66991a25e4ac1ac564.pdf
Azarbaijan Shahid Madani University
Communications in Combinatorics and Optimization
2538-2128
2538-2136
2
2
2017
09
01
Graceful labelings of the generalized Petersen graphs
149
159
EN
Aleksander
Vesel
University of Maribor
veselfnm@gmail.com
Zehui
Shao
School of Information Science & Technology, Chengdu University, Chengdu, China
zshao@gzhu.edu.cn
Fei
Deng
College of Information Science and Technology, Chengdu University of Technology, Chengdu, China
dengfei@cdut.cn
Zepeng
Li
Key Laboratory of High Confidence Software Technologies, Peking University, Peking, China
lizepeng@pku.edu.cn
10.22049/cco.2017.25918.1055
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.
graceful labeling,generalized Petersen graph,heuristic
http://comb-opt.azaruniv.ac.ir/article_13646.html
http://comb-opt.azaruniv.ac.ir/article_13646_07d33d001066dc9b0e695120e6125c8a.pdf