University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
49
2
2017
11
30
A novel algorithm to determine the leaf (leaves) of a binary tree from its preorder and postorder traversals
1
11
EN
N.
Aghaieabiane
Department of Engineering, School of Computer Science, New Jersey Institute of Technology,
Newark, New Jersey, the USA.
niloofaraghaie@ut.ac.ir, na396@njit.edu
H.
Koppelaar
0000-0001-7487-6564
Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of
Technology, Delft, The Netherlands.
koppelaar.henk@gmail.com
Peyman
Nasehpour
Department of Engineering Science, Golpayegan University of Technology, Golpayegan, Iran.
nasehpour@gut.ac.ir, nasehpour@gmail.com
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.
Binary tree,Proper binary tree,Preorder traversal,Inorder
traversal,Postorder traversal,time complexity,Space complexity
https://jac.ut.ac.ir/article_7972.html
https://jac.ut.ac.ir/article_7972_996a4abc640c11c9bc81d345f8955a5b.pdf
University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
49
2
2017
12
01
Super Pair Sum Labeling of Graphs
13
22
EN
R.
Vasuki
Department of Mathematics, Dr. Sivanthi Aditanar College of Engineering, Tiruchendur-628 215,Tamil Nadu, INDIA
vasukisehar@gmail.com
S.
Arockiaraj
Department of Mathematics, Mepco Schlenk Engineering College, Sivakasi-626124, Tamil Nadu
sarockiaraj\_77@yahoo.com
P.
Sugirtha
Department of Mathematics
Dr. Sivanthi Aditanar College of Engineering Tiruchendur-628 215,Tamil Nadu, INDIA.
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.html
https://jac.ut.ac.ir/article_7973_8d78e786bf0f7d9b317ea709b3d29cf1.pdf
University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
49
2
2017
12
01
Just chromatic exellence in fuzzy graphs
23
32
EN
M.
Dharmalingam
Department of Mathematics, The Madura College, Madurai
kmdharma6902@yahoo.in
R.
Udaya Suriya
Department of Mathematics, The Madura College, Madurai
udayasurya20@gmail.com
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}. <br />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 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.
fuzzy chromatic excellent,fuzzy just excel-
lent,fuzzy colorful vertex
https://jac.ut.ac.ir/article_7974.html
https://jac.ut.ac.ir/article_7974_949f55a87e6818f3a126579f601e0e54.pdf
University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
49
2
2017
12
01
Vulnerability Measure of a Network - a Survey
33
40
EN
Dara
Moazzami
University of Tehran, College of Engineering, Department of Engineering Science
dmoazzami@ut.ac.ir
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.
connectivity,Tenacity,binding number
https://jac.ut.ac.ir/article_7975.html
https://jac.ut.ac.ir/article_7975_bba7e5357a514c367cc5494c16287dc0.pdf
University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
49
2
2017
12
01
k-Remainder Cordial Graphs
41
52
EN
R.
Ponraj
Department of Mathematics, Sri Paramakalyani College, Alwarkurichi--627 412, India
ponrajmaths@gmail.com
K.
Annathurai
Department of Mathematics, Thiruvalluvar College, Papanasam--627 425, India
kannathuraitvcmaths@gmail.com
R.
Kala
Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli-- 627 012, India
karthipyi91@yahoo.co.in
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.
Path,cycle,Star,Bistar,Crown,Comb,complete graph
https://jac.ut.ac.ir/article_7976.html
https://jac.ut.ac.ir/article_7976_cc187cb94e0d46cf3e46d78a35564977.pdf
University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
49
2
2017
12
23
A new indexed approach to render the attractors of Kleinian groups
53
62
EN
Alessandro
Rosa
Software Developer
alessandro.a.rosa@gmail.com
One widespread procedure to render the attractor of Kleinian groups, appearing in the renown book [8], wants<br />huge 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.html
https://jac.ut.ac.ir/article_7977_a6c98d2207729c4747c1eafd480fa5a7.pdf
University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
49
2
2017
12
01
Solving a non-convex non-linear optimization problem constrained by fuzzy relational equations and Sugeno-Weber family of t-norms
63
101
EN
Amin
Ghodousian
Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, Iran
a.ghodousian@ut.ac.ir
A.
Ahmadi
Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, Iran
ahmadi91@ut.ac.ir
A.
Dehghani
Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, Iran
ali.dehghani@ut.ac.ir
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
Fuzzy relational equations,nonlinear optimization,genetic algorithm
https://jac.ut.ac.ir/article_7978.html
https://jac.ut.ac.ir/article_7978_699476726464c0890fc1bd731369b4c2.pdf
University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
49
2
2017
12
01
New Algorithm For Computing Secondary Invariants of Invariant Rings of Monomial Groups
103
111
EN
Sajjad
Rahmany
School of Mathematics and Computer Science,
Damghan University, Department of Mathematics, Damghan University,P.O. Box 36715-364,
Damghan, Iran.
rahmany@du.ac.ir
Abdolali
Basiri
School of Mathematics and Computer Science,
Damghan University, Department of Mathematics, Damghan University,P.O. Box 36715-364,
Damghan, Iran.
basiri@du.ac.ir
Behzad
Salehian
School of Mathematics and Computer Science,
Damghan University, Department of Mathematics, Damghan University,P.O. Box 36715-364,
Damghan, Iran.
bsalehian@du.ac.ir
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.
Invariant Ring,Secondary Invariant,SAGBI-\G basis,Monomial Groups,Algorithm F5-invariant
https://jac.ut.ac.ir/article_7982.html
https://jac.ut.ac.ir/article_7982_3c780e70c49fe47bd2911f087a31af61.pdf
University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
49
2
2017
12
01
Vibration Analysis of Global Near-regular Mechanical Systems
113
118
EN
Iman
Shojaei
Department of Biomedical Engineering, University of Kentucky, Lexington, KY 40506, USA.
shojaei.iman@uky.edu
Hossein
Rahami
0000-0001-7540-8412
School of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran.
hrahami@ut.ac.ir
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.
Global near-regular systems,Vibration analysis, Eigensolution,Kronecker products,Matrix operations
https://jac.ut.ac.ir/article_7983.html
https://jac.ut.ac.ir/article_7983_7ee73c94287e8a876e0cf6f78f198011.pdf
University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
49
2
2017
12
01
Some Properties of $(1,2)^*$-Soft\ b-Connected Spaces
119
127
EN
N.
Revathi
Department of Mathematics,\ Rani Anna Govt. College,\ Tirunelveli,\ India.
revmurugan83@gmail.com
K.
Bageerathi
Department of Mathematics, Aditanar College of Arts and Science, Tiruchendur, India.
mcrsm5678@rediff.mail
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
$(1,2)^*$-sb-separated,2)^*$-sb-connected,2)^*$-sb-compact
https://jac.ut.ac.ir/article_7985.html
https://jac.ut.ac.ir/article_7985_b554a90b10686dd186b8048ed362dc43.pdf
University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
49
2
2017
12
01
Group ${1, -1, i, -i}$ Cordial Labeling of sum of $C_n$ and $K_m$ for some $m$
129
139
EN
M.K.Karthik
Chidambaram
Department of Mathematics, St.Xavier's College ,Palayamkottai 627 002, Tamil Nadu, India
S.
Athisayanathan
Department of Mathematics, St.Xavier's College ,Palayamkottai 627 002, Tamil Nadu, India
R.
Ponraj
Department of Mathematics, Sri Paramakalyani College, Alwarkurichi--627 412, India
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.html
https://jac.ut.ac.ir/article_67017_4c8517321b4a9ce0092fceadfd46dd0e.pdf
University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
49
2
2017
12
01
Normalized Tenacity and Normalized Toughness of Graphs
141
159
EN
A.
Javan
University of Tehran, College of Engineering, Faculty of Engineerng Science, Department of Algorithms and Computation
ajavan@ut.ac.ir
M.
Jafarpour
0000-0001-7266-5018
University of Tehran, College of Engineering, Faculty of Engineerng Science, Department of Algorithms and Computation
m.jafarpour@ut.ac.ir
D.
Moazzami
Department of Algorithms and Computation, Faculty of Engineering Science, School of Engineering, University of Tehran, Iran,
dmoazzami@ut.ac.ir
A.
Moieni
University of Tehran, College of Engineering, Faculty of Engineerng Science, Department of Algorithms and Computation
moeini@ut.ac.ir
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.html
https://jac.ut.ac.ir/article_67083_3fd2ac811babd8cee9e72ba5576224a0.pdf