A novel algorithm to determine the leaf (leaves) of a binary tree from its preorder and postorder traversals N. Aghaieabiane Department of Engineering, School of Computer Science, New Jersey Institute of Technology, Newark, New Jersey, the USA. author H. Koppelaar Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands. author Peyman Nasehpour Department of Engineering Science, Golpayegan University of Technology, Golpayegan, Iran. author text article 2017 eng 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. Journal of Algorithms and Computation University of Tehran 2476-2776 49 v. 2 no. 2017 1 11 https://jac.ut.ac.ir/article_7972_996a4abc640c11c9bc81d345f8955a5b.pdf Super Pair Sum Labeling of Graphs R. Vasuki Department of Mathematics, Dr. Sivanthi Aditanar College of Engineering, Tiruchendur-628 215,Tamil Nadu, INDIA author S. Arockiaraj Department of Mathematics, Mepco Schlenk Engineering College, Sivakasi-626124, Tamil Nadu author P. Sugirtha Department of Mathematics Dr. Sivanthi Aditanar College of Engineering Tiruchendur-628 215,Tamil Nadu, INDIA. author text article 2017 eng 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. Journal of Algorithms and Computation University of Tehran 2476-2776 49 v. 2 no. 2017 13 22 https://jac.ut.ac.ir/article_7973_8d78e786bf0f7d9b317ea709b3d29cf1.pdf Just chromatic exellence in fuzzy graphs M. Dharmalingam Department of Mathematics, The Madura College, Madurai author R. Udaya Suriya Department of Mathematics, The Madura College, Madurai author text article 2017 eng 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  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. Journal of Algorithms and Computation University of Tehran 2476-2776 49 v. 2 no. 2017 23 32 https://jac.ut.ac.ir/article_7974_949f55a87e6818f3a126579f601e0e54.pdf Vulnerability Measure of a Network - a Survey Dara Moazzami University of Tehran, College of Engineering, Department of Engineering Science author text article 2017 eng 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. Journal of Algorithms and Computation University of Tehran 2476-2776 49 v. 2 no. 2017 33 40 https://jac.ut.ac.ir/article_7975_bba7e5357a514c367cc5494c16287dc0.pdf k-Remainder Cordial Graphs R. Ponraj Department of Mathematics, Sri Paramakalyani College, Alwarkurichi--627 412, India author K. Annathurai Department of Mathematics, Thiruvalluvar College, Papanasam--627 425, India author R. Kala Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli-- 627 012, India author text article 2017 eng 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. Journal of Algorithms and Computation University of Tehran 2476-2776 49 v. 2 no. 2017 41 52 https://jac.ut.ac.ir/article_7976_cc187cb94e0d46cf3e46d78a35564977.pdf A new indexed approach to render the attractors of Kleinian groups Alessandro Rosa Software Developer author text article 2017 eng One widespread procedure to render the attractor of Kleinian groups, appearing in the renown book , 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. Journal of Algorithms and Computation University of Tehran 2476-2776 49 v. 2 no. 2017 53 62 https://jac.ut.ac.ir/article_7977_a6c98d2207729c4747c1eafd480fa5a7.pdf Solving a non-convex non-linear optimization problem constrained by fuzzy relational equations and Sugeno-Weber family of t-norms Amin Ghodousian Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, Iran author A. Ahmadi Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, Iran author A. Dehghani Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, Iran author text article 2017 eng 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 Journal of Algorithms and Computation University of Tehran 2476-2776 49 v. 2 no. 2017 63 101 https://jac.ut.ac.ir/article_7978_699476726464c0890fc1bd731369b4c2.pdf New Algorithm For Computing Secondary Invariants of Invariant Rings of Monomial Groups Sajjad Rahmany School of Mathematics and Computer Science, Damghan University, Department of Mathematics, Damghan University,P.O. Box 36715-364, Damghan, Iran. author Abdolali Basiri School of Mathematics and Computer Science, Damghan University, Department of Mathematics, Damghan University,P.O. Box 36715-364, Damghan, Iran. author Behzad Salehian School of Mathematics and Computer Science, Damghan University, Department of Mathematics, Damghan University,P.O. Box 36715-364, Damghan, Iran. author text article 2017 eng 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. Journal of Algorithms and Computation University of Tehran 2476-2776 49 v. 2 no. 2017 103 111 https://jac.ut.ac.ir/article_7982_3c780e70c49fe47bd2911f087a31af61.pdf Vibration Analysis of Global Near-regular Mechanical Systems Iman Shojaei Department of Biomedical Engineering, University of Kentucky, Lexington, KY 40506, USA. author Hossein Rahami School of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran. author text article 2017 eng 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. Journal of Algorithms and Computation University of Tehran 2476-2776 49 v. 2 no. 2017 113 118 https://jac.ut.ac.ir/article_7983_7ee73c94287e8a876e0cf6f78f198011.pdf Some Properties of $(1,2)^*$-Soft\\ b-Connected Spaces N. Revathi Department of Mathematics,\ Rani Anna Govt. College,\ Tirunelveli,\ India. author K. Bageerathi Department of Mathematics, Aditanar College of Arts and Science, Tiruchendur, India. author text article 2017 eng 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 Journal of Algorithms and Computation University of Tehran 2476-2776 49 v. 2 no. 2017 119 127 https://jac.ut.ac.ir/article_7985_b554a90b10686dd186b8048ed362dc43.pdf Group $\{1, -1, i, -i\}$ Cordial Labeling of sum of $C_n$ and $K_m$ for some $m$ M.K.Karthik Chidambaram Department of Mathematics, St.Xavier&#039;s College ,Palayamkottai 627 002, Tamil Nadu, India author S. Athisayanathan Department of Mathematics, St.Xavier&#039;s College ,Palayamkottai 627 002, Tamil Nadu, India author R. Ponraj Department of Mathematics, Sri Paramakalyani College, Alwarkurichi--627 412, India author text article 2017 eng 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. Journal of Algorithms and Computation University of Tehran 2476-2776 49 v. 2 no. 2017 129 139 https://jac.ut.ac.ir/article_67017_4c8517321b4a9ce0092fceadfd46dd0e.pdf Normalized Tenacity and Normalized Toughness of Graphs A. Javan University of Tehran, College of Engineering, Faculty of Engineerng Science, Department of Algorithms and Computation author M. Jafarpour University of Tehran, College of Engineering, Faculty of Engineerng Science, Department of Algorithms and Computation author D. Moazzami Department of Algorithms and Computation, Faculty of Engineering Science, School of Engineering, University of Tehran, Iran, author A. Moieni University of Tehran, College of Engineering, Faculty of Engineerng Science, Department of Algorithms and Computation author text article 2017 eng 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. Journal of Algorithms and Computation University of Tehran 2476-2776 49 v. 2 no. 2017 141 159 https://jac.ut.ac.ir/article_67083_3fd2ac811babd8cee9e72ba5576224a0.pdf