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
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, 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.
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
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-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}.
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 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.
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