ORIGINAL_ARTICLE
$Z_k$-Magic Labeling of Some Families of Graphs
For any non-trivial abelian group A under addition a graph $G$ is said to be $A$-\textit{magic} if there exists a labeling $f:E(G) \rightarrow A-\{0\}$ such that, the vertex labeling $f^+$ defined as $f^+(v) = \sum f(uv)$ taken over all edges $uv$ incident at $v$ is a constant. An $A$-\textit{magic} graph $G$ is said to be $Z_k$-magic graph if the group $A$ is $Z_k$ the group of integers modulo $k$. These $Z_k$-magic graphs are referred to as $k$-\textit{magic} graphs. In this paper we prove that the total graph, flower graph, generalized prism graph, closed helm graph, lotus inside a circle graph, $G\odot\overline{K_m}$, $m$-splitting graph of a path and $m$-shadow graph of a path are $Z_k$-magic graphs.
https://jac.ut.ac.ir/article_69046_6280f6ffe52fb49581c3603a8b60a45f.pdf
2018-12-30
1
12
A-magic labeling
$Z_k$-magic labeling
$Z_k$-magic graph
total graph
flower graph
generalized prism graph
closed helm graph
lotus inside a circle graph
$Godotoverline{K_m}$
$m$-splitting graph
$m$-shadow graph
P.
Jeyanthi
jeyajeyanthi@rediffmail.com
1
Principal and Head of the Research Centre,Department of Mathematics,Govindammal Aditanar College for Women,Tiruchendur,Tamilnadu,INDIA
LEAD_AUTHOR
K.
Jeyadaisy
jeyadaisy@yahoo.com
2
Department of Mathematics Holy Cross College, Nagercoil, Tamilnadu, India.
AUTHOR
ORIGINAL_ARTICLE
Linear programming on SS-fuzzy inequality constrained problems
In this paper, a linear optimization problem is investigated whose constraints are defined with fuzzy relational inequality. These constraints are formed as the intersection of two inequality fuzzy systems and Schweizer-Sklar family of t-norms. Schweizer-Sklar family of t-norms is a parametric family of continuous t-norms, which covers the whole spectrum of t-norms when the parameter is changed from zero to infinity. Firstly, we investigate the resolution of the feasible region of the problem and studysome theoretical results. A necessary and sufficient condition and three other necessary conditions are derived for determining the feasibility. Moreover, in order to simplify the problem, some procedures are presented. It is proved that the optimal solution of the problem is always resulted from the unique maximum solution and a minimal solution of the feasible region. A method is proposed to generate random feasible max-Schweizer-Sklar fuzzy relational inequalities and an algorithm is presented to solve the problem. Finally, an example is described to illustrate these algorithms.
https://jac.ut.ac.ir/article_69466_597a69e191920561fefb09353557c2f2.pdf
2018-12-30
13
36
Fuzzy relation
fuzzy relational inequality
linear optimization
fuzzy compositions and t-norms
Amin
Ghodousian
a.ghodousian@ut.ac.ir
1
University of Tehran, College of Engineering, Faculty of Engineering Science
LEAD_AUTHOR
shahrzad
oveisi
shahrzad.oveisi@gmail.com
2
Department of Algorithms and Computation, University of Tehran,Tehran, Iran.
AUTHOR
ORIGINAL_ARTICLE
Snakes and Caterpillars in Graceful Graphs
Graceful labelings use a prominent place among difference vertex labelings. In this work we present new families of graceful graphs all of them obtained applying a general substitution result. This substitution is applied here to replace some paths with some trees with a more complex structures. Two caterpillars with the same size are said to be \textit{analogous} if thelarger stable sets, in both caterpillars, have the same cardinality. We studythe conditions that allow us to replace, within a gracefully labeled graph,some snakes (or paths) by analogous caterpillars, to produce a new gracefulgraph. We present five families of graphs where this replacement isfeasible, generalizing in this way some existing results: subdivided trees, first attachment trees, path-like trees, two-point union of paths, and armed crowns.
https://jac.ut.ac.ir/article_69503_bd9e68d1fedd8b959976b68013ae5357.pdf
2018-12-30
37
47
a-labeling
graceful labeling
snake
caterpillar. & & %vspace{0.1cm} end{tabular}
Christian
Barrientos
chr_barrientos@yahoo.com
1
Department of Mathematics, Valencia College, Orlando, FL, 32825, USA.
LEAD_AUTHOR
Sarah
Minion
sarah.m.minion@gmail.com
2
Department of Mathematics, Valencia College, Orlando, FL, 32825, USA
AUTHOR
ORIGINAL_ARTICLE
$4$-Total prime cordial labeling of some cycle related graphs
Let $G$ be a $(p,q)$ graph. Let $f:V(G)\to\{1,2, \ldots, k\}$ be a map where $k \in \mathbb{N}$ and $k>1$. For each edge $uv$, assign the label $\gcd(f(u),f(v))$. $f$ is called $k$-Total prime cordial labeling of $G$ if $\left|t_{f}(i)-t_{f}(j)\right|\leq 1$, $i,j \in \{1,2, \cdots,k\}$ where $t_{f}(x)$ denotes the total number of vertices and the edges labelled with $x$. A graph with a $k$-total prime cordial labeling is called $k$-total prime cordial graph. In this paper we investigate the $4$-total prime cordial labeling of some graphs like Prism, Helm, Dumbbell graph, Sun flower graph.
https://jac.ut.ac.ir/article_69777_b697bb2042469a4545ccaf731813c86a.pdf
2018-12-30
49
57
Prism
Helm
Dumbbell graph
Sun flower graph
R
Ponraj
ponrajmaths@gmail.com
1
Department of Mathematics Sri Parakalyani College Alwarkurichi -627 412, India
LEAD_AUTHOR
J
Maruthamani
mmani2011@gmail.com
2
Research Scholar, Register number: 18124012091054, Department of Mathematics, Manonmaniam sundarnar university, Abishekapatti, Tirunelveli-627012, Tamilnadu, India
AUTHOR
ORIGINAL_ARTICLE
LP problems constrained with D-FRIs
In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated where the feasible region is formed as the intersection of two inequality fuzzy systems and Dombi family of t-norms is considered as fuzzy composition. Dombi family of t-norms includes a parametric family of continuous strict t-norms, whose members are increasing functions of the parameter. This family of t-norms covers the whole spectrum of t-norms when the parameter is changed from zero to infinity. The resolution of the feasible region of the problem is firstly investigated when it is defined with max-Dombi composition. Based on some theoretical results, a necessary and sufficient condition and three other necessary conditions are derived for determining the feasibility. Moreover, in order to simplify the problem, some procedures are presented. It is shown that a lower bound is always attainable for the optimal objective value. Also, it is proved that the optimal solution of the problem is always resulted from the unique maximum solution and a minimal solution of the feasible region. A method is proposed to generate random feasible max-Dombi fuzzy relational inequalities and an algorithm is presented to solve the problem. Finally, an example is described to illustrate these algorithms.
https://jac.ut.ac.ir/article_69778_67019cccd3ae9e759e6e2c4861660c90.pdf
2018-12-30
59
79
Fuzzy relation
fuzzy relational inequality
linear optimization
fuzzy compositions and t-norms
A.
Ghodousian
a.ghodousian@ut.ac.ir
1
Faculty of Engineering Science, College of Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran
LEAD_AUTHOR
M.
Jafarpour
m.jafarpour@ut.ac.ir
2
University of Tehran, College of Engineering, Faculty of Engineerng Science, Department of Algorithms and Computation
AUTHOR
ORIGINAL_ARTICLE
Tenacity and some other Parameters of Interval Graphs can be computed in polynomial time
In general, computation of graph vulnerability parameters is NP-complete. In past, some algorithms were introduced to prove that computation of toughness, scattering number, integrity and weighted integrity parameters of interval graphs are polynomial.
In this paper, two different vulnerability parameters of graphs, tenacity and rupture degree are defined.
In general, computing the tenacity of a graph is NP-hard and the rupture degree of a graph is NP-complete, but in this paper, we will show that these parameters can be computed in polynomial time for interval graphs.
https://jac.ut.ac.ir/article_69783_125974741bf455d35e0263d2b3b55ef5.pdf
2018-12-30
81
87
Vulnerability parameters
Tenacity
rupture degree
Interval graphs
Dara
Moazzami
dmoazzami@ut.ac.ir
1
University of Tehran, College of Engineering, Faculty of Engineering Science
LEAD_AUTHOR
Niloofar
Vahdat
vahdat_n@alumni.ut.ac.ir
2
University of Tehran, Department of Algorithms and Computation
AUTHOR
ORIGINAL_ARTICLE
Inverse eigenvalue problem for matrices whose graph is a banana tree
In this paper, we consider an inverse eigenvalue problem (IEP) for constructing a special kind of acyclic matrices. The problem involves the reconstruction of matrices whose graph is a banana tree. This is performed by using the minimal and maximal eigenvalues of all leading principal submatrices of the required matrix. The necessary and sufficient conditionsfor the solvability of the problem is derived. An algorithm to construct the solution is provided.
https://jac.ut.ac.ir/article_69994_2c6384790926c12c2f8526d4ea76dc44.pdf
2018-12-30
89
101
Inverse eigenvalue problem
banana tree
leading principal minors
eigenvalue
graph of a matrix
Maryam
Babaei Zarch
maryam.babaei@stu.yazd.ac.ir
1
Department of Computer Science, Yazd University, Yazd, Iran.
AUTHOR
Seyed Abolfazl
Shahzadeh Fazeli
fazeli@yazd.ac.ir
2
Department of Computer Science, Yazd University, Yazd, Iran.
LEAD_AUTHOR
Seyed Mehdi
Karbassi
smkarbassi@yazd.ac.ir
3
Department of Mathematical Science, Yazd University, Yazd, Iran.
AUTHOR
ORIGINAL_ARTICLE
Minimizing the Number of Tardy Jobs on Single Machine Scheduling with Flexible Maintenance Time
In this study, single machine scheduling with flexible maintenance is investigated with non-resumable jobs by minimizing the weighted number of tardy jobs. It is assumed that the machine stops for a constant interval time during the scheduling period to perform maintenance. In other words, the starting time of maintenance is the decision variable. By reviewing the literature, we noticed that this problem has not been studied yet. Initially, it is proved that the problem is NP-hard. Then, a mathematical model is proposed and solved by the GAMS software. Because of the long time for solving the problem with an exact method, we develop a heuristic algorithm. To evaluate the efficiency of the proposed algorithm, 696 test problems with different sizes of the problem in the range from 1 to 2000 jobs, are generated. The computational results demonstrate that the average error of solution is 10.93\%.
https://jac.ut.ac.ir/article_70449_f9a5d9d44b0de2068a18eff346e228c3.pdf
2018-12-30
103
119
Scheduling
Single machine
Flexible maintenance
Tardy job
Fatemeh
Ganji
ganji@gut.ac.ir
1
Department of Industrial Engineering, Gopayegan University of Technology. Golpayegan, Iran
LEAD_AUTHOR
Amir
Jamali
ajamali@gut.ac.ir
2
Department of Industrial Engineering, Gopayegan University of Technology. Golpayegan, Iran
AUTHOR
ORIGINAL_ARTICLE
Sign Test for Fuzzy Random Variables
This paper extends the sign test to the case where data are observations of fuzzy random variables, and the hypotheses are imprecise rather than crisp. In this approach, first a new notion of fuzzy random variables is introduced. Then, the $\alpha$-level sets of the imprecise observations are transacted to extend the usual method of sign test. To do this, the concepts of fuzzy median and fuzzy sample median are defined.We also develop a well-known large sample property of the classical sample median. In addition, the test statistic is extended for investigating fuzzy hypothesis. After that, applying an index called credibility degree, the degree that the observed fuzzy test statistics belongs to the critical region is evaluated. The result provides a fuzzy test function which leads to some degrees to accept or to reject the fuzzy null hypothesis.A numerical example is provided to clarify the discussions made in this paper.
https://jac.ut.ac.ir/article_70450_0a2fe9c34dd4bab68198b0dde50a274c.pdf
2018-12-30
121
139
Sign test
fuzzy median
fuzzy sample median
fuzzy test statistic
credibility index
optimistic value
degree of belonging
Mehdi
Shams
mehdishams@kashanu.ac.ir
1
Department of Mathematical Sciences, University of Kashan, Isfahan, Iran.
LEAD_AUTHOR
Gholamreza
Hesamian
gh.hesamian@pnu.ac.ir
2
Department of Statistics, Payame Noor University, Tehran, 19395-3697, Iran.
AUTHOR
ORIGINAL_ARTICLE
Changes in Artificial Neural Network Learning Parameters and Their Impact on Modeling Error Reduction
The main objective of this research is to investigate the effect of neural network architecture parameters on model behavior. Neural network architectural factors such as training algorithm, number of hidden layer neurons, data set design in training stage and the changes made to them, and finally its effect on the output of the model were investigated. It developed a database for modeling using by multi-layer perceptron. In particular, the modeling process enjoyed three training algorithms: Bayesian Regularization (BR), Scaled Conjugate Gradient (SCG) and Levenberg Marquardt (LM). Model selection criteria based on the lowest error rate and data regression, using a trial and error approach. The results showed that models that greatly reduce the error have less generalizability. In the meantime, the BR algorithm with the data set design of 15-15-70 (for test, validation and training sections, respectively), has been used to reduce the error better than other algorithms, but improper generalizability. In contrast, the LM algorithm has better generalizability than the other two algorithms. Data analysis shows that, in most cases, when the amounts of data dedicated to test and validation change (increase or decrease), the model requires more neurons in order to reduce errors.
https://jac.ut.ac.ir/article_70904_d98c02626eb1d645dbddd9b9ccc2beb0.pdf
2018-12-30
141
155
Somayeh
Mehrabadi
somayeh.mehrabadi@yahoo.com
1
Free scholar
LEAD_AUTHOR