University of Tehran Journal of Algorithms and Computation 2476-2776 54 1 2022 06 01 Pair mean cordial labeling of graphs 1 10 87392 10.22059/jac.2022.87392 EN R Ponraj Department of Mathematics Sri Parakalyani College Alwarkurichi -627 412, India S Prabhu Research Scholor, Reg.No: 21121232091003, Department of Mathematics, Sri Paramakalyani College, Alwarkurichi&ndash;627 412, Tamilnadu, India Journal Article 2022 05 25 In this paper, we introduce a new graph labeling called pair mean cordial labeling of graphs. Also, we investigate the pair mean cordiality of some graphs like path, cycle, complete graph, star, wheel, ladder, and comb. https://jac.ut.ac.ir/article_87392_1826c7cf2b60089d62aa5b172956101a.pdf
University of Tehran Journal of Algorithms and Computation 2476-2776 54 1 2022 06 01 A comparison between the resolution and linear optimization of FREs defined by product t-norm and geometric mean operator 11 22 87918 10.22059/jac.2022.87918 EN Amin Ghodousian Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, Iran. Sara Falahatkar Department of Engineering Science, College of Engineering, University of Tehran Journal Article 2022 06 30 In this paper, a type of fuzzy system is firstly investigated whereby the feasible region is defined by the fuzzy relational equalities and the geometric mean as fuzzy composition. Some related basic and theoretical properties of such fuzzy relational equations are derived and the feasible region is completely determined. Also, it is proved that the feasible solutions set can be stated by one maximum solution and a finite number of minimal solutions. Moreover, a comparison is made between this region and fuzzy relational equations defined by the product t-norm. Finally, an example is described to illustrate the differences of these two FRE systems. https://jac.ut.ac.ir/article_87918_932bdf407c8c8cd879b38fb914cd068d.pdf
University of Tehran Journal of Algorithms and Computation 2476-2776 54 1 2022 06 01 Developing a New Genetic Algorithm for Selecting Efficient Project Portfolio 23 34 87942 10.22059/jac.2022.87942 EN Mohammad Mirabi Department of Industrial Engineering, Meybod University, Meybod, Iran Mohammad Reza Zare Banadkouki Department of Industrial Engineering, Faculty of Engineering, Meybod University, Meybod, Iran Journal Article 2022 07 02 selecting an efficient project portfolio among available projects is a vital decision for any project manager. The main questions are which projects can have more long-term benefits for managers or organizations. Due to the complexity of this field of research, today so many approaches are developed for project selection. Calculation time and the quality of results are two main criteria that almost all researchers have considered on them. In this research, a new hybrid genetic algorithm with new heuristic mutation and cross-over is developed to choose a good portfolio of available projects. The presented algorithm is fast and effective to reach a good result in a reasonable time. Finding a good point to start as an initial population and using a good operator a heuristic mutation and cross-over are the main points of our algorithm. To check the quality of results we compare the developed algorithms with some recent ones in the literature and comparison studies and statistical calculation demonstrate the efficiency of the new genetic algorithm to select a good portfolio.   https://jac.ut.ac.ir/article_87942_d9b3be4ba6dcbddd0b3b1640a380be99.pdf
University of Tehran Journal of Algorithms and Computation 2476-2776 54 1 2022 06 01 \$4\$-total mean cordial labeling of union of some graphs with the complete bipartite graph \$K_{2,n}\$ 35 46 88026 10.22059/jac.2022.88026 EN R Ponraj Department of Mathematics Sri Parakalyani College Alwarkurichi -627 412, India S SUBBULAKSHMI Sri Paramakalyani College Alwarkurichi-627412, Tamilnadu, India S Somasundaram Department of Mathematics Manonmaniam sundarnar university, Abishekapatti, Tirunelveli-627012, Tamilnadu, India Journal Article 2022 07 06 Let \$G\$ be a graph. Let \$f:Vleft(Gright)rightarrow left{0,1,2,ldots,k-1right}\$ be a function where \$kin mathbb{N}\$ and \$k>1\$. For each edge \$uv\$, assign the label \$fleft(uvright)=leftlceil frac{fleft(uright)+fleft(vright)}{2}rightrceil\$. \$f\$ is called \$k\$-total mean cordial labeling of \$G\$ if \$left|t_{mf}left(iright)-t_{mf}left(jright) right| leq 1\$, for all \$i,jinleft{0,1,2,ldots,k-1right}\$, where \$t_{mf}left(xright)\$ denotes the total number of vertices and edges labelled with \$x\$, \$xinleft{0,1,2,ldots,k-1right}\$. A graph with admit a \$k\$-total mean cordial labeling is called \$k\$-total mean cordial graph. In this paper, we investigate the \$4\$-total mean cordial labeling of some graphs derived from the complete bipartite graph \$K_{2,n}\$. https://jac.ut.ac.ir/article_88026_b4a0c112be1a111aca23842002f29f95.pdf
University of Tehran Journal of Algorithms and Computation 2476-2776 54 1 2022 06 01 A Survey on Tenacity Parameter\Part II 47 72 88027 10.22059/jac.2022.88027 EN Dara Moazzami University of Tehran, College of Engineering, Faculty of Engineering Science. Asieh Khoshnood University of Tehran Department of Algorihthms and Computation, Tehran, Iran Journal Article 2022 07 06 In this paper, we study the edge tenacity of graphs. We will be primarily<br />interested in edge-tenacious graphs, which can be considered very stable and are somewhat analogous in edge tenacity<br />to honest graphs in edge-integrity. We show several results about edge-tenacious graphs as well as<br />find numerous classes of edge-tenacious graphs.<br />The Cartesian Products of graphs like hypercube, grids, and tori are widely used to design interconnection networks in multiprocessor computing systems.<br />These considerations motivated us to study tenacity of Cartesian products of graphs. We find the tenacity of Cartesian product of complete graphs (thus setting a conjecture stated in Cozzens and al.) and grids.<br />The Middle Graph, M(G) of a graph G is the graph obtained from G by inserting a new vertex into every edge of G and by joining by edges those pairs of these new vertices which lie on adjacent edges of G<br />  https://jac.ut.ac.ir/article_88027_7aabe4f5b8610fd31d2ec24c291c6d86.pdf
University of Tehran Journal of Algorithms and Computation 2476-2776 54 1 2022 06 01 Comparison of solutions resulted from direct problems formulated as FRE 73 87 88038 10.22059/jac.2022.88038 EN Amin Ghodousian Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, Iran. Sara Zal College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, Iran. Journal Article 2022 07 07 In this paper, we investigate direct solution of FRE and compare their results with expected real consequences. We give an applied example formulated by a FRE problem and show that FRE defined by maximum t-conorm and an arbitrary t-norm can yield different interpretations for our example. A necessary condition and a sufficient condition are presented that guarantee FRE defined by maximum t-conorm and minimum t-norm attain the same solutions as human mind does. Also, we present a t-conorm and use it instead of maximum t-conorm in FRE to obtain solutions with highest similarity with real ones. Finally, we show that under some conditions, FRE defined by any t-conorm and any t-norm may find a solution which is not reasonable. https://jac.ut.ac.ir/article_88038_1854bbcd808bbf0954cc710f98d12240.pdf
University of Tehran Journal of Algorithms and Computation 2476-2776 54 1 2022 06 01 Approximating the Number of Lattice Points inside a Regular Polygon 89 98 88337 10.22059/jac.2022.88337 EN Mahdi Imanparast Department of Computer Science, University of Bojnord, Bojnord, Iran Journal Article 2022 07 30 We study the problem of counting the number of lattice points inside a regular polygon with \$n\$ sides when its center is at the origin and present an exact algorithm with \$mathcal{O}(k^{2}log n)\$ time and two approximate answers for this problem, where \$k\$ is the absolute value of side length of the minimum bounding box of the regular polygon. Numerical results show the efficiency of the approximations in calculating the answer to this problem. https://jac.ut.ac.ir/article_88337_67dd7eac844ccf9796bf5fca36033f08.pdf
University of Tehran Journal of Algorithms and Computation 2476-2776 54 1 2022 06 01 Relative Clustering Coefficient 99 108 88373 10.22059/jac.2022.88373 EN Elena Touli Department of Mathematics, Stockholm University Oscar Lindberg Department of Mathematics, Stockholm university Journal Article 2022 08 02 In this paper, we relatively extend the definition of the global clustering coefficient to another clustering, which we call it emph{relative clustering coefficient}. The idea of this definition is to ignore the edges in the network that the probability of having an edge is \$0\$. Here, we also consider a model as an example that using the relative clustering coefficient is better than the global clustering coefficient for comparing networks and also checking the properties of the networks. https://jac.ut.ac.ir/article_88373_3d678c3dff380dbd41d09aa352638319.pdf
University of Tehran Journal of Algorithms and Computation 2476-2776 54 1 2022 06 01 An iterative method and maximal solution of Coupled algebraic Riccati equations 109 123 88374 10.22059/jac.2022.88374 EN Hajar Alimorad Department of Mathematics, Jahrom University, P.O. Box: 74135-111, Iran. Journal Article 2022 08 02 Coupled Riccati equation has widely been applied to various engineering areas such as jump linear quadratic problem, particle transport theory, and Wiener–Hopf decomposition of Markov chains. In this paper, we consider an iterative method for computing the Hermitian solution of the Coupled Algebraic Riccati Equations (CARE) which is usually encountered in control theory. We show some properties of this iterative method. Furthermore, it will also be demonstrated that the maximal solution can be obtained numerically via a certain linear or quadratic inequalities optimization problem. Numerical examples are presented and the results are compared. https://jac.ut.ac.ir/article_88374_bf25d25fdbc416b40db31da3b13f85c5.pdf
University of Tehran Journal of Algorithms and Computation 2476-2776 54 1 2022 06 01 Speeding up the Arc Consistency algorithm in Constraint Satisfaction Problems: A New Modification of AC-3 125 138 88375 10.22059/jac.2022.88375 EN Yaser Shokri Kalandaragh, Department of Advanced Technologies, University of Mohaghegh Ardabili. Journal Article 2022 08 02 Dealing with constraints is always very common in real-world implementation issues. Search algorithms for real problems are also no exception. Because of the constraints in search problems (named Constraint Satisfaction Problems (CSPs)), their main solving algorithm is presented in backtracking form. The constraint propagation algorithm is an auxiliary tool to avoid facing constraint conditions as well as reducing search options. This algorithm has been presented in almost seven versions so far. In this paper, we have updated the third version of this algorithm, which is presented under the title of AC-3, from five aspects and have increased its capabilities. The most important feature of our proposed algorithm is its low time complexity. This feature has been made possible by two auxiliary criteria introduction for detecting more critical binary constraints. Faster investigation of critical constraints leads to early detection of dead-end in the search path and the search continues in this direction stops. https://jac.ut.ac.ir/article_88375_d4de1325c79b435b9a2b15e4529ed812.pdf