University of TehranJournal of Algorithms and Computation2476-277649220171130A novel algorithm to determine the leaf (leaves) of a binary tree from its preorder and postorder traversals111797210.22059/jac.2017.7972ENN. AghaieabianeDepartment of Engineering, School of Computer Science, New Jersey Institute of Technology,
Newark, New Jersey, the USA.H. KoppelaarFaculty of Electrical Engineering, Mathematics and Computer Science, Delft University of
Technology, Delft, The Netherlands.0000-0001-7487-6564Peyman NasehpourDepartment of Engineering Science, Golpayegan University of Technology, Golpayegan, Iran.Journal Article20170630Binary 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.pdfUniversity of TehranJournal of Algorithms and Computation2476-277649220171201Super Pair Sum Labeling of Graphs1322797310.22059/jac.2017.7973ENR. VasukiDepartment of Mathematics, Dr. Sivanthi Aditanar College of Engineering, Tiruchendur-628 215,Tamil Nadu, INDIAS. ArockiarajDepartment of Mathematics, Mepco Schlenk Engineering College, Sivakasi-626124, Tamil NaduP. SugirthaDepartment of Mathematics
Dr. Sivanthi Aditanar College of Engineering Tiruchendur-628 215,Tamil Nadu, INDIA.Journal Article20170208Let $G$ 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.pdfUniversity of TehranJournal of Algorithms and Computation2476-277649220171201Just chromatic exellence in fuzzy graphs2332797410.22059/jac.2017.7974ENM. DharmalingamDepartment of Mathematics, The Madura College, MaduraiR. Udaya SuriyaDepartment of Mathematics, The Madura College, MaduraiJournal Article20170422A 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}. <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 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.pdfUniversity of TehranJournal of Algorithms and Computation2476-277649220171201Vulnerability Measure of a Network - a Survey3340797510.22059/jac.2017.7975ENDara MoazzamiUniversity of Tehran, College of Engineering, Department of Engineering ScienceJournal Article20170303In 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.pdfUniversity of TehranJournal of Algorithms and Computation2476-277649220171201k-Remainder Cordial Graphs4152797610.22059/jac.2017.7976ENR. PonrajDepartment of Mathematics, Sri Paramakalyani College, Alwarkurichi--627 412, IndiaK. AnnathuraiDepartment of Mathematics, Thiruvalluvar College, Papanasam--627 425, IndiaR. KalaDepartment of Mathematics, Manonmaniam Sundaranar University, Tirunelveli-- 627 012, IndiaJournal Article20170630In 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.pdfUniversity of TehranJournal of Algorithms and Computation2476-277649220171223A new indexed approach to render the attractors of Kleinian groups5362797710.22059/jac.2017.7977ENAlessandro RosaSoftware Developer0000-0001-7942-5092Journal Article20170630One 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_a6c98d2207729c4747c1eafd480fa5a7.pdfUniversity of TehranJournal of Algorithms and Computation2476-277649220171201Solving a non-convex non-linear optimization problem constrained by fuzzy relational equations and Sugeno-Weber family of t-norms63101797810.22059/jac.2017.7978ENAmin GhodousianFaculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, Iran0000-0002-9224-8470A. AhmadiFaculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, IranA. DehghaniFaculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, IranJournal Article20170310Sugeno-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 FREshttps://jac.ut.ac.ir/article_7978_699476726464c0890fc1bd731369b4c2.pdfUniversity of TehranJournal of Algorithms and Computation2476-277649220171201New Algorithm For Computing Secondary Invariants of Invariant Rings of Monomial Groups103111798210.22059/jac.2017.7982ENSajjad RahmanySchool of Mathematics and Computer Science,
Damghan University, Department of Mathematics, Damghan University,P.O. Box 36715-364,
Damghan, Iran.Abdolali BasiriSchool of Mathematics and Computer Science,
Damghan University, Department of Mathematics, Damghan University,P.O. Box 36715-364,
Damghan, Iran.Behzad SalehianSchool of Mathematics and Computer Science,
Damghan University, Department of Mathematics, Damghan University,P.O. Box 36715-364,
Damghan, Iran.Journal Article20161116In 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.pdfUniversity of TehranJournal of Algorithms and Computation2476-277649220171201Vibration Analysis of Global Near-regular Mechanical Systems113118798310.22059/jac.2017.7983ENIman ShojaeiDepartment of Biomedical Engineering, University of Kentucky, Lexington, KY 40506, USA.Hossein RahamiSchool of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran.0000-0001-7540-8412Journal Article20170302Some 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.pdfUniversity of TehranJournal of Algorithms and Computation2476-277649220171201Some Properties of $(1,2)^*$-Soft\\ b-Connected Spaces119127798510.22059/jac.2017.7985ENN. RevathiDepartment of Mathematics,\ Rani Anna Govt. College,\ Tirunelveli,\ India.K. BageerathiDepartment of Mathematics, Aditanar College of Arts and Science, Tiruchendur, India.Journal Article20160917In 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 spacehttps://jac.ut.ac.ir/article_7985_b554a90b10686dd186b8048ed362dc43.pdfUniversity of TehranJournal of Algorithms and Computation2476-277649220171201Group $\{1, -1, i, -i\}$ Cordial Labeling of sum of $C_n$ and $K_m$ for some $m$1291396701710.22059/jac.2017.67017ENM.K.Karthik ChidambaramDepartment of Mathematics, St.Xavier's College ,Palayamkottai 627 002, Tamil Nadu, IndiaS. AthisayanathanDepartment of Mathematics, St.Xavier's College ,Palayamkottai 627 002, Tamil Nadu, IndiaR. PonrajDepartment of Mathematics, Sri Paramakalyani College, Alwarkurichi--627 412, IndiaJournal Article20161208Let 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.pdfUniversity of TehranJournal of Algorithms and Computation2476-277649220171201Normalized Tenacity and Normalized Toughness of Graphs1411596708310.22059/jac.2017.67083ENA. JavanUniversity of Tehran, College of Engineering, Faculty of Engineerng Science, Department of Algorithms and ComputationM. JafarpourUniversity of Tehran, College of Engineering, Faculty of Engineerng Science, Department of Algorithms and Computation0000-0001-7266-5018D. MoazzamiDepartment of Algorithms and Computation, Faculty of Engineering Science, School of Engineering, University of Tehran, Iran,A. MoieniUniversity of Tehran, College of Engineering, Faculty of Engineerng Science, Department of Algorithms and Computation0000-0002-6408-3525Journal Article20170107In 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