### فهرست مطالب

• Volume:54 Issue: 1, Jun 2022
• تاریخ انتشار: 1401/04/18
• تعداد عناوین: 10
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• R .Ponraj *, S .Prabhu Pages 1-10

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.

Keywords: Path, cycle, complete graph, Wheel, ladder, Comb, Star, Bistar, fan graph
• Amin Ghodousian *, Sara Falahatkar Pages 11-22
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.
Keywords: Fuzzy relational equalities, fuzzy compositions, t-norm, geometric mean operator, linear optimization

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.

Keywords: Project portfolio, New Genetic Algorithm, Heuristic Mutation, Heuristic Cross over
• R .Ponraj *, S .SUBBULAKSHMI, S. Somasundaram Pages 35-46

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 $K_{2,n}$.

Keywords: Path, cycle, complete graph, Star, Bistar, Fan, Wheel, helm, ladder
• Dara Moazzami *, Asieh Khoshnood Pages 47-72
In this paper, we study the edge tenacity of graphs. We will be primarilyinterested in edge-tenacious graphs, which can be considered very stable and are somewhat analogous in edge tenacityto honest graphs in edge-integrity. We show several results about edge-tenacious graphs as well asfind numerous classes of edge-tenacious graphs.The Cartesian Products of graphs like hypercube, grids, and tori are widely used to design interconnection networks in multiprocessor computing systems.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.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
Keywords: edge-tenacious, Cartesian products, Middle Graph, connectivity, binding number, toughness, maximum graphical structure
• Amin Ghodousian *, Sara Zal Pages 73-87
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.
Keywords: Fuzzy relation, composition of fuzzy relations, Fuzzy relational equations, and Fuzzy operators
• Mahdi Imanparast Pages 89-98

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 O(k2logn) 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.

Keywords: Guass's circle problem, lattice points, regular polygons, approximation algorithms
• Elena Touli, Oscar Lindberg Pages 99-108

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.

Keywords: The global clustering coefficient, local clustering coefficient, relative clustering coefficient networks, and graphs

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.

Keywords: Coupled algebraic Riccati equations, Maximal solution, Positive semidefinite matrix
• Yaser Shokri Kalandaragh Pages 125-138

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.

Keywords: Search Algorithm, Constraint Satisfaction, Constraint Propagation, Arc Consistency, Binary Constraint