2018-07-20T09:30:56Z
http://comb-opt.azaruniv.ac.ir/?_action=export&rf=summon&issue=2233
Communications in Combinatorics and Optimization
Commun. Comb. Opt.
2538-2128
2538-2128
2017
2
2
Primal-dual path-following algorithms for circular programming
Baha
Alzalg
Mohammad
Pirhaji
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
2017
09
01
65
85
http://comb-opt.azaruniv.ac.ir/article_13631_3b92d66c63867691344b503a2f0746f7.pdf
Communications in Combinatorics and Optimization
Commun. Comb. Opt.
2538-2128
2538-2128
2017
2
2
Reformulated F-index of graph operations
Hamideh
Aram
Nasrin
Dehgardi
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
2017
09
01
87
98
http://comb-opt.azaruniv.ac.ir/article_13630_719b7afc30e723e9cbae02669009d3c6.pdf
Communications in Combinatorics and Optimization
Commun. Comb. Opt.
2538-2128
2538-2128
2017
2
2
On leap Zagreb indices of graphs
Ivan
Gutman
Ahmed
Naji
Nandappa
Soner
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
2017
09
01
99
117
http://comb-opt.azaruniv.ac.ir/article_13643_fc88ed6fdf52b7f7a7ad4b621f695992.pdf
Communications in Combinatorics and Optimization
Commun. Comb. Opt.
2538-2128
2538-2128
2017
2
2
Some results on the complement of a new graph associated to a commutative ring
S.
Visweswaran
Anirudhdha
Parmar
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
2017
09
01
119
138
http://comb-opt.azaruniv.ac.ir/article_13644_1b27eaa14546119e0ee5915425b1cb0b.pdf
Communications in Combinatorics and Optimization
Commun. Comb. Opt.
2538-2128
2538-2128
2017
2
2
Approximation Solutions for Time-Varying Shortest Path Problem
Gholam Hassan
Shirdel
Hassan
Rezapour
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
2017
09
01
139
147
http://comb-opt.azaruniv.ac.ir/article_13645_0d39e0bfe8ae0a66991a25e4ac1ac564.pdf
Communications in Combinatorics and Optimization
Commun. Comb. Opt.
2538-2128
2538-2128
2017
2
2
Graceful labelings of the generalized Petersen graphs
Aleksander
Vesel
Zehui
Shao
Fei
Deng
Zepeng
Li
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
2017
09
01
149
159
http://comb-opt.azaruniv.ac.ir/article_13646_07d33d001066dc9b0e695120e6125c8a.pdf