ORIGINAL_ARTICLE
A novel algorithm to determine the leaf (leaves) of a binary tree from its preorder and postorder traversals
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 BT-LEAF, a novel one, to detect the leaf (leaves) of a binary tree from its preorder and postorder traversals in quadratic time and linear space.
https://jac.ut.ac.ir/article_7972_996a4abc640c11c9bc81d345f8955a5b.pdf
2017-11-30
1
11
Binary tree
Proper binary tree
Preorder traversal
Inorder
traversal
Postorder traversal
time complexity
Space complexity
N.
Aghaieabiane
niloofaraghaie@ut.ac.ir, na396@njit.edu
1
Department of Engineering, School of Computer Science, New Jersey Institute of Technology, Newark, New Jersey, the USA.
AUTHOR
H.
Koppelaar
koppelaar.henk@gmail.com
2
Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands.
AUTHOR
Peyman
Nasehpour
nasehpour@gut.ac.ir, nasehpour@gmail.com
3
Department of Engineering Science, Golpayegan University of Technology, Golpayegan, Iran.
AUTHOR
ORIGINAL_ARTICLE
Super Pair Sum Labeling of Graphs
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 $\{0, \pm 1, \pm2, \dots, \pm (\frac{p+q-1}{2})\}$ 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.
https://jac.ut.ac.ir/article_7973_8d78e786bf0f7d9b317ea709b3d29cf1.pdf
2017-12-01
13
22
R.
Vasuki
vasukisehar@gmail.com
1
Department of Mathematics, Dr. Sivanthi Aditanar College of Engineering, Tiruchendur-628 215,Tamil Nadu, INDIA
AUTHOR
S.
Arockiaraj
sarockiaraj\_77@yahoo.com
2
Department of Mathematics, Mepco Schlenk Engineering College, Sivakasi-626124, Tamil Nadu
AUTHOR
P.
Sugirtha
3
Department of Mathematics Dr. Sivanthi Aditanar College of Engineering Tiruchendur-628 215,Tamil Nadu, INDIA.
AUTHOR
ORIGINAL_ARTICLE
Just chromatic exellence in fuzzy graphs
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 1965\cite{zl} and further studied\cite{ka}. It was Rosenfeld\cite{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 studied\cite{mss}. Computing chromatic sum of an arbitrary graph introduced by Kubica [1989] is known as NP-complete 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 coloring\cite{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. R\cite{sls}. In this paper we are introducing \textquotedblleft Just Chromatic excellence in fuzzy graphs\textquotedblright.
https://jac.ut.ac.ir/article_7974_949f55a87e6818f3a126579f601e0e54.pdf
2017-12-01
23
32
fuzzy chromatic excellent
fuzzy just excel-
lent
fuzzy colorful vertex
M.
Dharmalingam
kmdharma6902@yahoo.in
1
Department of Mathematics, The Madura College, Madurai
LEAD_AUTHOR
R.
Udaya Suriya
udayasurya20@gmail.com
2
Department of Mathematics, The Madura College, Madurai
AUTHOR
ORIGINAL_ARTICLE
Vulnerability Measure of a Network - a Survey
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.
https://jac.ut.ac.ir/article_7975_bba7e5357a514c367cc5494c16287dc0.pdf
2017-12-01
33
40
connectivity
Tenacity
binding number
Dara
Moazzami
dmoazzami@ut.ac.ir
1
University of Tehran, College of Engineering, Department of Engineering Science
LEAD_AUTHOR
ORIGINAL_ARTICLE
k-Remainder Cordial Graphs
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.
https://jac.ut.ac.ir/article_7976_cc187cb94e0d46cf3e46d78a35564977.pdf
2017-12-01
41
52
Path
cycle
Star
Bistar
Crown
Comb
complete graph
R.
Ponraj
ponrajmaths@gmail.com
1
Department of Mathematics, Sri Paramakalyani College, Alwarkurichi--627 412, India
LEAD_AUTHOR
K.
Annathurai
kannathuraitvcmaths@gmail.com
2
Department of Mathematics, Thiruvalluvar College, Papanasam--627 425, India
AUTHOR
R.
Kala
karthipyi91@yahoo.co.in
3
Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli-- 627 012, India
AUTHOR
ORIGINAL_ARTICLE
A new indexed approach to render the attractors of Kleinian groups
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.
https://jac.ut.ac.ir/article_7977_a6c98d2207729c4747c1eafd480fa5a7.pdf
2017-12-23
53
62
Alessandro
Rosa
alessandro.a.rosa@gmail.com
1
Software Developer
LEAD_AUTHOR
ORIGINAL_ARTICLE
Solving a non-convex non-linear optimization problem constrained by fuzzy relational equations and Sugeno-Weber family of t-norms
Sugeno-Weber family of t-norms and t-conorms is one of the most applied one in various fuzzy modelling problems. This family of t-norms and t-conorms was suggested by Weber for modeling intersection and union of fuzzy sets. Also, the t-conorms were suggested as addition rules by Sugeno for so-called $\lambda$–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 Sugeno-Weber t-norm. We firstly investigate the resolution of the feasible region when it is defined with max-Sugeno-Weber 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
https://jac.ut.ac.ir/article_7978_699476726464c0890fc1bd731369b4c2.pdf
2017-12-01
63
101
Fuzzy relational equations
nonlinear optimization
genetic algorithm
Amin
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
A.
Ahmadi
ahmadi91@ut.ac.ir
2
Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, Iran
AUTHOR
A.
Dehghani
ali.dehghani@ut.ac.ir
3
Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, Iran
AUTHOR
ORIGINAL_ARTICLE
New Algorithm For Computing Secondary Invariants of Invariant Rings of Monomial Groups
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 SAGBI-\G 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 well-suited to complexity analysis and very easy to implement.
https://jac.ut.ac.ir/article_7982_3c780e70c49fe47bd2911f087a31af61.pdf
2017-12-01
103
111
Invariant Ring
Secondary Invariant
SAGBI-G basis
Monomial Groups
Algorithm F5-invariant
Sajjad
Rahmany
rahmany@du.ac.ir
1
School of Mathematics and Computer Science, Damghan University, Department of Mathematics, Damghan University,P.O. Box 36715-364, Damghan, Iran.
AUTHOR
Abdolali
Basiri
basiri@du.ac.ir
2
School of Mathematics and Computer Science, Damghan University, Department of Mathematics, Damghan University,P.O. Box 36715-364, Damghan, Iran.
AUTHOR
Behzad
Salehian
bsalehian@du.ac.ir
3
School of Mathematics and Computer Science, Damghan University, Department of Mathematics, Damghan University,P.O. Box 36715-364, Damghan, Iran.
LEAD_AUTHOR
ORIGINAL_ARTICLE
Vibration Analysis of Global Near-regular Mechanical Systems
Some near-regular mechanical systems involve global deviations from their corresponding regular system. Despite extensive research on vibration analysis (eigensolution) of regular and local near-regular mechanical systems, the literature on vibration analysis of global near-regular 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.
https://jac.ut.ac.ir/article_7983_7ee73c94287e8a876e0cf6f78f198011.pdf
2017-12-01
113
118
Global near-regular systems
Vibration analysis, Eigensolution
Kronecker products
Matrix operations
Iman
Shojaei
shojaei.iman@uky.edu
1
Department of Biomedical Engineering, University of Kentucky, Lexington, KY 40506, USA.
AUTHOR
Hossein
Rahami
hrahami@ut.ac.ir
2
School of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran.
LEAD_AUTHOR
ORIGINAL_ARTICLE
Some Properties of $(1,2)^*$-Soft\\ b-Connected Spaces
In this paper we introduce the concept of $(1,2)^*$-sb-separated sets and $(1,2)^*$-soft b-connected 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
https://jac.ut.ac.ir/article_7985_b554a90b10686dd186b8048ed362dc43.pdf
2017-12-01
119
127
$(1
2)^*$-sb-separated
2)^*$-sb-connected
2)^*$-sb-compact
N.
Revathi
revmurugan83@gmail.com
1
Department of Mathematics,\ Rani Anna Govt. College,\ Tirunelveli,\ India.
LEAD_AUTHOR
K.
Bageerathi
mcrsm5678@rediff.mail
2
Department of Mathematics, Aditanar College of Arts and Science, Tiruchendur, India.
AUTHOR
ORIGINAL_ARTICLE
Group $\{1, -1, i, -i\}$ Cordial Labeling of sum of $C_n$ and $K_m$ for some $m$
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.
https://jac.ut.ac.ir/article_67017_4c8517321b4a9ce0092fceadfd46dd0e.pdf
2017-12-01
129
139
M.K.Karthik
Chidambaram
1
Department of Mathematics, St.Xavier's College ,Palayamkottai 627 002, Tamil Nadu, India
AUTHOR
S.
Athisayanathan
2
Department of Mathematics, St.Xavier's College ,Palayamkottai 627 002, Tamil Nadu, India
AUTHOR
R.
Ponraj
3
Department of Mathematics, Sri Paramakalyani College, Alwarkurichi--627 412, India
AUTHOR
ORIGINAL_ARTICLE
Normalized Tenacity and Normalized Toughness of Graphs
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.
https://jac.ut.ac.ir/article_67083_3fd2ac811babd8cee9e72ba5576224a0.pdf
2017-12-01
141
159
A.
Javan
ajavan@ut.ac.ir
1
University of Tehran, College of Engineering, Faculty of Engineerng Science, Department of Algorithms and Computation
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
D.
Moazzami
dmoazzami@ut.ac.ir
3
Department of Algorithms and Computation, Faculty of Engineering Science, School of Engineering, University of Tehran, Iran,
AUTHOR
A.
Moieni
moeini@ut.ac.ir
4
University of Tehran, College of Engineering, Faculty of Engineerng Science, Department of Algorithms and Computation
AUTHOR