JOURNAL OF ALGORITHMS AND COMPUTATION
Year:2018 | Volume:50 | Issue:2|Papers Count:9

For any non-trivial abelian group A under addition a graph G is said to be A-magic if there exists a labeling f: E(G) → A − {0} such that, the vertex labeling f+ defined as f+(v) = P f(uv) taken over all edges uv incident at v is a constant. An A-magic graph G is said to be Zk-magic graph if the group A is Zk the group of integers modulo k. These Zk-magic graphs are referred to as k-magic graphs. In this paper we prove that the total graph, flower graph, generalized prism graph, closed helm graph, lotus inside a circle graph, G ⊙ Km, m-splitting graph of a path and m-shadow graph of a path are Zk-magic graphs.

In this paper, a linear optimization problem is investigated whose constraints are de ned with fuzzy relational inequality. These constraints are formed as the intersection of two inequality fuzzy systems and Schweizer-Sklar family of t-norms. Schweizer-Sklar family of t-norms is a parametric family of continuous t-norms, which covers the whole spectrum of t-norms when the parameter is changed from zero to in nity. Firstly, we investigate the resolution of the feasible region of the problem and studysome theoretical results. A necessary and su cient condition and three other necessary conditions are derived for determining the feasibility. Moreover, in order to simplify the problem, some procedures are presented. It is proved that the optimal solution of the problem is always resulted from the unique maximum solution and a minimal solution of the feasible region. A method

Graceful labelings use a prominent place among di er-ence vertex labelings. In this work we present new fam-ilies of graceful graphs all of them obtained applying a general substitution result. This substitution is ap-plied here to replace some paths with some trees with a more complex structures. Two caterpillars with the same size are said to be analogous if the larger stable sets, in both caterpillars, have the same cardinality. We study the conditions that allow us to replace, within a gracefully labeled graph, some snakes (or paths) by anal-ogous caterpillars, to produce a new graceful graph. We present  ve families of graphs where this replacement is feasible, generalizing in this way some existing results: subdivided trees,  rst attachment trees, path-like trees, two-point union of paths, and armed crowns.

Let G be a (p; q) graph. Let f: V (G)! f1; 2; : : :; kg be a map where k 2 N and k > 1. For each edge uv, assign the label gcd(f(u); f(v)). f is called k-Total prime cordial labeling of G if jtf (i) 􀀀 tf (j)j  1, i; j 2 f1; 2;


; kg where tf (x) denotes the total number of vertices and the edges labelled with x. A graph with a k-total prime cordial labeling is called k-total prime cordial graph. In this paper we investigate the 4-total prime cordial labeling of some graphs like Prism, Helm, Dumbbell graph, Sun ower graph.

In this paper, optimization of a linear objective func-tion with fuzzy relational inequality constraints is in-vestigated where the feasible region is formed as the in-tersection of two inequality fuzzy systems and Dombi family of t-norms is considered as fuzzy composition. Dombi family of t-norms includes a parametric family of continuous strict t-norms, whose members are increas-ing functions of the parameter. This family of t-norms covers the whole spectrum of t-norms when the param-eter is changed from zero to in nity. The resolution of the feasible region of the problem is  rstly investigated when it is de ned with max-Dombi composition. Based on some theoretical results, a necessary and su cient condition and three other necessary conditions are de-rived for determining the feasibility. Moreover, in order to simplify the problem, some procedures are presented.

In general, computation of graph vulnerability parameters is NP-complete. In past, some algorithms were introduced to prove that computation of toughness, scattering number, integrity and weighted integrity parameters of interval graphs are polynomial. In this paper, two di erent vulnerability parameters of graphs, tenacity and rupture degree are de ned. In general, computing the tenacity of a graph is NP-hard and the rupture degree of a graph is NP-complete, but in this paper, we will show that these parameters can be computed in polynomial time for interval graphs.

In this paper, we consider an inverse eigenvalue problem (IEP) for constructing a special kind of acyclic matri-ces. The problem involves the reconstruction of matri-ces whose graph is a banana tree. This is performed by using the minimal and maximal eigenvalues of all lead-ing principal submatrices of the required matrix. The necessary and su cient conditions for the solvability of the problem is derived. An algorithm to construct the solution is provided.

In this study, single machine scheduling with exible maintenance is investigated with non-resumable jobs by minimizing the weighted number of tardy jobs. It is assumed that the machine stops for a constant interval time during the scheduling period to perform mainte-nance. In other words, the starting time of maintenance is the decision variable. By reviewing the literature, we noticed that this problem has not been studied yet. Ini-tially, it is proved that the problem is NP-hard. Then, a mathematical model is proposed and solved by the GAMS software. Because of the long time for solving the problem with an exact method, we develop a heuris-tic algorithm.

This paper extends the sign test to the case where data are observations of fuzzy random variables, and the hypotheses are imprecise rather than crisp. In this approach,  rst a new notion of fuzzy random variables is introduced. Then, the -level sets of the imprecise observations are transacted to extend the usual method of sign test. To do this, the concepts of fuzzy median and fuzzy sample median are de ned. We also develop a well-known large sample property of the classical sample median. In addition, the test statistic is extended for investigating fuzzy hypothesis. After that, applying an index called credibility degree, the degree that the observed fuzzy test statistics belongs to the critical region is evaluated. The result provides a fuzzy test function which leads to some degrees to accept or to reject the fuzzy null hypothesis. A numerical example is provided to clarify the discussions made in this paper.