2017
2
2
0
95
Primaldual pathfollowing algorithms for circular programming
2
2
Circular programming problems are a new class of convex optimization problems that include secondorder cone programming problems as a special case. Alizadeh and Goldfarb [Math. Program. Ser. A 95 (2003) 351] introduced primaldual pathfollowing algorithms for solving secondorder 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 primaldual pathfollowing 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 selfconcordant barrier. The numerical examples show the pathfollowing algorithms are simple and efficient.
1

65
85


Baha
Alzalg
The University of Jordan
The University of Jordan
Jordan
baha2math@gmail.com


Mohammad
Pirhaji
Shahrekord University
Shahrekord University
Iran
mojtabapirhaji@yahoo.com
Circular cone programming
Interior point methods
Euclidean Jordan algebra
Selfconcordance
Reformulated Findex of graph operations
2
2
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 Findex. Similarly, reformulated first general Zagreb index is defined in terms of edgedrees as $EM_1^lambda(G)=sum_{ein E(G)}d_{G}(e)^lambda$ and the reformulated Findex is $RF(G)=sum_{ein E(G)}d_{G}(e)^3$. In this paper, we compute the reformulated Findex for some graph operations.
1

87
98


Hamideh
Aram
Department of Mathematics
Gareziaeddin Center, Khoy Branch, Islamic Azad University, Khoy, Iran
Department of Mathematics
Gareziaeddin Center,
Iran
hamideh.aram@gmail.com


Nasrin
Dehgardi
Department of Mathematics and Computer Science,
Sirjan University of Technology
Sirjan, I.R. Iran
Department of Mathematics and Computer Science,
Iran
ndehgardi@gmail.com
First general Zagreb index
reformulated first general Zagreb index
Findex
reformulated Findex
On leap Zagreb indices of graphs
2
2
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.
1

99
117


Ivan
Gutman
University of Kragujevac
University of Kragujevac
Serbia
gutman@kg.ac.rs


Ahmed
Naji
Department of Mathematics, University of Mysore, Mysusu, India
Department of Mathematics, University of
India
ama.mohsen78@gmail.com


Nandappa
Soner
Department of Mathematics, University of Mysore, Mysuru, India
Department of Mathematics, University of
India
ndsoner@yahoo.co.in
degree (of vertex)
Second degree
Zagreb indices
leap Zagreb indices
Some results on the complement of a new graph associated to a commutative ring
2
2
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 theoreticproperties of R.
1

119
138


S.
Visweswaran
Saurashtra University
Saurashtra University
India
s_visweswaran2006@yahoo.co.in


Anirudhdha
Parmar
Saurashtra University
Saurashtra University
India
anirudh.maths@gmail.com
Annihilating ideal of a ring
maximal Nprime of (0)
connected graph
diameter. girth
Approximation Solutions for TimeVarying Shortest Path Problem
2
2
Abstract. Timevarying network optimization problems have traditionally been solved by specialized algorithms. These algorithms have NPcomplement time complexity. This paper considers the timevarying shortest 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}.
1

139
147


Gholam Hassan
Shirdel
University of Qom
University of Qom
Iran
shirdel81math@gmail.com


Hassan
Rezapour
Unuversity of Qom
Unuversity of Qom
Iran
hassan.rezapour@gmail.com
TimeVarying Optimization
Approximation solutions
Shortest Path Problem
Graceful labelings of the generalized Petersen graphs
2
2
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.
1

149
159


Aleksander
Vesel
University of Maribor
University of Maribor
Slovenia
veselfnm@gmail.com


Zehui
Shao
School of Information Science & Technology, Chengdu University, Chengdu, China
School of Information Science & Technology
China
zshao@gzhu.edu.cn


Fei
Deng
College of Information Science and Technology, Chengdu University of Technology, Chengdu, China
College of Information Science and Technology,
China
dengfei@cdut.cn


Zepeng
Li
Key Laboratory of High Confidence Software Technologies, Peking University, Peking, China
Key Laboratory of High Confidence Software
China
lizepeng@pku.edu.cn
graceful labeling
generalized Petersen graph
heuristic