2017
49
2
2
0
1

A novel algorithm to determine the leaf (leaves) of a binary tree from its preorder and postorder traversals
https://jac.ut.ac.ir/article_7972.html
1
Binary trees are essential structures in Computer Science. The leaf (leaves) of a binary tree is one of the most significant aspects of it. In this study, we prove that the order of a leaf (leaves) of a binary tree is the same in the main tree traversals; preorder, inorder, and postorder. Then, we prove that given the preorder and postorder traversals of a binary tree, the leaf (leaves) of a binary tree can be determined. We present the algorithm BTLEAF, a novel one, to detect the leaf (leaves) of a binary tree from its preorder and postorder traversals in quadratic time and linear space.
0

1
11


N.
Aghaieabiane
Department of Engineering, School of Computer Science, New Jersey Institute of Technology,
Newark, New Jersey, the USA.
Iran
niloofaraghaie@ut.ac.ir, na396@njit.edu


H.
Koppelaar
Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of
Technology, Delft, The Netherlands.
Iran
koppelaar.henk@gmail.com


Peyman
Nasehpour
Department of Engineering Science, Golpayegan University of Technology, Golpayegan, Iran.
Iran
nasehpour@gut.ac.ir, nasehpour@gmail.com
Binary tree
Proper binary tree
Preorder traversal
Inorder traversal
Postorder traversal
time complexity
Space complexity
1

Super Pair Sum Labeling of Graphs
https://jac.ut.ac.ir/article_7973.html
1
Let $G$ be a graph with $p$ vertices and $q$ edges. The graph $G$ is said to be a super pair sum labeling if there exists a bijection $f$ from $V(G)cup E(G)$ to ${0, pm 1, pm2, dots, pm (frac{p+q1}{2})}$ when $p+q$ is odd and from $V(G)cup E(G)$ to ${pm 1, pm 2, dots, pm (frac{p+q}{2})}$ when $p+q$ is even such that $f(uv)=f(u)+f(v).$ A graph that admits a super pair sum labeling is called a {it super pair sum graph}. Here we study about the super pair sum labeling of some standard graphs.
0

13
22


R.
Vasuki
Department of Mathematics, Dr. Sivanthi Aditanar College of Engineering, Tiruchendur628 215,Tamil Nadu, INDIA
Iran
vasukisehar@gmail.com


S.
Arockiaraj
Department of Mathematics, Mepco Schlenk Engineering College, Sivakasi626124, Tamil Nadu
Iran
sarockiaraj\_77@yahoo.com


P.
Sugirtha
Department of Mathematics
Dr. Sivanthi Aditanar College of Engineering Tiruchendur628 215,Tamil Nadu, INDIA.
Iran
1

Just chromatic exellence in fuzzy graphs
https://jac.ut.ac.ir/article_7974.html
1
A fuzzy graph is a symmetric binary fuzzy relation on a fuzzy subset. The concept of fuzzy sets and fuzzy relations was introduced by L.A.Zadeh in 1965cite{zl} and further studiedcite{ka}. It was Rosenfeldcite{ra} who considered fuzzy relations on fuzzy sets and developed the theory of fuzzy graphs in 1975. The concepts of fuzzy trees, blocks, bridges and cut nodes in fuzzy graph has been studiedcite{mss}. Computing chromatic sum of an arbitrary graph introduced by Kubica [1989] is known as NPcomplete problem. Graph coloring is the most studied problem of combinatorial optimization. As an advancement fuzzy coloring of a fuzzy graph was defined by authors Eslahchi and Onagh in 2004, and later developed by them as Fuzzy vertex coloringcite{eo} in 2006.This fuzzy vertex coloring was extended to fuzzy total coloring in terms of family of fuzzy sets by Lavanya. S and Sattanathan. Rcite{sls}. In this paper we are introducing textquotedblleft Just Chromatic excellence in fuzzy graphstextquotedblright.
0

23
32


M.
Dharmalingam
Department of Mathematics, The Madura College, Madurai
Iran
kmdharma6902@yahoo.in


R.
Udaya Suriya
Department of Mathematics, The Madura College, Madurai
Iran
udayasurya20@gmail.com
fuzzy chromatic excellent
fuzzy just excel lent
fuzzy colorful vertex
1

Vulnerability Measure of a Network  a Survey
https://jac.ut.ac.ir/article_7975.html
1
In this paper we discuss about tenacity and its properties in stability calculation. We indicate relationships between tenacity and connectivity, tenacity and binding number, tenacity and toughness. We also give good lower and upper bounds for tenacity. Since we are primarily interested in the case where disruption of the graph is caused by the removal of a vertex or vertices (and the resulting loss of all edges incident with the removed vertices), we shall restrict our discussion to vertex stability measures. In the interest of completeness, however, we have included several related measures of edge stability.
0

33
40


Dara
Moazzami
University of Tehran, College of Engineering, Department of Engineering Science
Iran
dmoazzami@ut.ac.ir
connectivity
Tenacity
binding number
1

kRemainder Cordial Graphs
https://jac.ut.ac.ir/article_7976.html
1
In this paper we generalize the remainder cordial labeling, called $k$remainder cordial labeling and investigate the $4$remainder cordial labeling behavior of certain graphs.
0

41
52


R.
Ponraj
Department of Mathematics, Sri Paramakalyani College, Alwarkurichi627 412, India
Iran
ponrajmaths@gmail.com


K.
Annathurai
Department of Mathematics, Thiruvalluvar College, Papanasam627 425, India
Iran
kannathuraitvcmaths@gmail.com


R.
Kala
Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli 627 012, India
Iran
karthipyi91@yahoo.co.in
Path
cycle
Star
Bistar
Crown
Comb
complete graph
1

A new indexed approach to render the attractors of Kleinian groups
https://jac.ut.ac.ir/article_7977.html
1
One widespread procedure to render the attractor of Kleinian groups, appearing in the renown book [8], wantshuge memory resources to compute and store the results. We present a new faster and lighter version that drops the original array and pulls out group elements from integers.
0

53
62


Alessandro
Rosa
Software Developer
Iran
alessandro.a.rosa@gmail.com
1

Solving a nonconvex nonlinear optimization problem constrained by fuzzy relational equations and SugenoWeber family of tnorms
https://jac.ut.ac.ir/article_7978.html
1
SugenoWeber family of tnorms and tconorms is one of the most applied one in various fuzzy modelling problems. This family of tnorms and tconorms was suggested by Weber for modeling intersection and union of fuzzy sets. Also, the tconorms were suggested as addition rules by Sugeno for socalled $lambda$–fuzzy measures. In this paper, we study a nonlinear optimization problem where the feasible region is formed as a system of fuzzy relational equations (FRE) defined by the SugenoWeber tnorm. We firstly investigate the resolution of the feasible region when it is defined with maxSugenoWeber composition and present some necessary and sufficient conditions for determining the feasibility of the problem. Also, two procedures are presented for simplifying the problem. Since the feasible solutions set of FREs
0

63
101


Amin
Ghodousian
Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 113654563, Tehran, Iran
Iran
a.ghodousian@ut.ac.ir


A.
Ahmadi
Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 113654563, Tehran, Iran
Iran
ahmadi91@ut.ac.ir


A.
Dehghani
Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 113654563, Tehran, Iran
Iran
ali.dehghani@ut.ac.ir
Fuzzy relational equations
nonlinear optimization
genetic algorithm
1

New Algorithm For Computing Secondary Invariants of Invariant Rings of Monomial Groups
https://jac.ut.ac.ir/article_7982.html
1
In this paper, a new algorithm for computing secondary invariants of invariant rings of monomial groups is presented. The main idea is to compute simultaneously a truncated SAGBIG basis and the standard invariants of the ideal generated by the set of primary invariants. The advantage of the presented algorithm lies in the fact that it is wellsuited to complexity analysis and very easy to implement.
0

103
111


Sajjad
Rahmany
School of Mathematics and Computer Science,
Damghan University, Department of Mathematics, Damghan University,P.O. Box 36715364,
Damghan, Iran.
Iran
rahmany@du.ac.ir


Abdolali
Basiri
School of Mathematics and Computer Science,
Damghan University, Department of Mathematics, Damghan University,P.O. Box 36715364,
Damghan, Iran.
Iran
basiri@du.ac.ir


Behzad
Salehian
School of Mathematics and Computer Science,
Damghan University, Department of Mathematics, Damghan University,P.O. Box 36715364,
Damghan, Iran.
Iran
bsalehian@du.ac.ir
Invariant Ring
Secondary Invariant
SAGBIG basis
Monomial Groups
Algorithm F5invariant
1

Vibration Analysis of Global Nearregular Mechanical Systems
https://jac.ut.ac.ir/article_7983.html
1
Some nearregular mechanical systems involve global deviations from their corresponding regular system. Despite extensive research on vibration analysis (eigensolution) of regular and local nearregular mechanical systems, the literature on vibration analysis of global nearregular mechanical systems is scant. In this paper, a method for vibration analysis of such systems was developed using Kronecker products and matrix manipulations. Specifically, the eigensolution of the corresponding regular mechanical system was inserted in the algorithm to further accelerate the solution. The developed method allowed reduction in computational complexity (i.e., $mathrm{O}(n^2)$) when compared to earlier methods. The application of the method was indicated using a simple example.
0

113
118


Iman
Shojaei
Department of Biomedical Engineering, University of Kentucky, Lexington, KY 40506, USA.
Iran
shojaei.iman@uky.edu


Hossein
Rahami
School of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran.
Iran
hrahami@ut.ac.ir
Global nearregular systems
Vibration analysis, Eigensolution
Kronecker products
Matrix operations
1

Some Properties of $(1,2)^*$Soft\ bConnected Spaces
https://jac.ut.ac.ir/article_7985.html
1
In this paper we introduce the concept of $(1,2)^*$sbseparated sets and $(1,2)^*$soft bconnected spaces and prove some properties related to these break topics. Also we disscused the properties of $(1,2)^*$soft b compactness in soft bitopological space
0

119
127


N.
Revathi
Department of Mathematics, Rani Anna Govt. College, Tirunelveli, India.
Iran
revmurugan83@gmail.com


K.
Bageerathi
Department of Mathematics, Aditanar College of Arts and Science, Tiruchendur, India.
Iran
mcrsm5678@rediff.mail
$(1
2)^*$sbseparated
2)^*$sbconnected
2)^*$sbcompact
1

Group ${1, 1, i, i}$ Cordial Labeling of sum of $C_n$ and $K_m$ for some $m$
https://jac.ut.ac.ir/article_67017.html
1
Let G be a (p,q) graph and A be a group. We denote the order of an element $a in A $ by $o(a).$ Let $ f:V(G)rightarrow A$ be a function. For each edge $uv$ assign the label 1 if $(o(f(u)),o(f(v)))=1 $or $0$ otherwise. $f$ is called a group A Cordial labeling if $v_f(a)v_f(b) leq 1$ and $e_f(0) e_f(1)leq 1$, where $v_f(x)$ and $e_f(n)$ respectively denote the number of vertices labelled with an element $x$ and number of edges labelled with $n (n=0,1).$ A graph which admits a group A Cordial labeling is called a group A Cordial graph. In this paper we define group ${1 ,1 ,i ,i}$ Cordial graphs and characterize the graphs $C_n + K_m (2 leq m leq 5)$ that are group ${1 ,1 ,i ,i}$ Cordial.
0

129
139


M.K.Karthik
Chidambaram
Department of Mathematics, St.Xavier's College ,Palayamkottai 627 002, Tamil Nadu, India
Iran


S.
Athisayanathan
Department of Mathematics, St.Xavier's College ,Palayamkottai 627 002, Tamil Nadu, India
Iran


R.
Ponraj
Department of Mathematics, Sri Paramakalyani College, Alwarkurichi627 412, India
Iran
1

Normalized Tenacity and Normalized Toughness of Graphs
https://jac.ut.ac.ir/article_67083.html
1
In this paper, we introduce the novel parameters indicating Normalized Tenacity ($T_N$) and Normalized Toughness ($t_N$) by a modification on existing Tenacity and Toughness parameters. Using these new parameters enables the graphs with different orders be comparable with each other regarding their vulnerabilities. These parameters are reviewed and discussed for some special graphs as well.
0

141
159


A.
Javan
University of Tehran, College of Engineering, Faculty of Engineerng Science, Department of Algorithms and Computation
Iran
ajavan@ut.ac.ir


M.
Jafarpour
University of Tehran, College of Engineering, Faculty of Engineerng Science, Department of Algorithms and Computation
Iran
m.jafarpour@ut.ac.ir


D.
Moazzami
Department of Algorithms and Computation, Faculty of Engineering Science, School of Engineering, University of Tehran, Iran,
Iran
dmoazzami@ut.ac.ir


A.
Moieni
University of Tehran, College of Engineering, Faculty of Engineerng Science, Department of Algorithms and Computation
Iran
moeini@ut.ac.ir