Discrete Mathematics and Combinatorics Commons^™

A Study Of Graphical Permutations, Jessica Thune

UNLV Theses, Dissertations, Professional Papers, and Capstones

A permutation π on a set of positive integers {a_1,a_2,...,a_n} is said to be graphical if there exists a graph containing exactly a_i vertices of degree (a_i) for each i. It has been shown that for positive integers with a_1

Generalizations Of Pascal's Triangle: A Construction Based Approach, Michael Anton Kuhlmann

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The study of this paper is based on current generalizations of Pascal's Triangle, both the expansion of the polynomial of one variable and the multivariate case. Our goal is to establish relationships between these generalizations, and to use the properties of the generalizations to create a new type of generalization for the multivariate case that can be represented in the third dimension.

In the first part of this paper we look at Pascal's original Triangle with properties and classical applications. We then look at contemporary extensions of the triangle to coefficient arrays for polynomials of two forms. The first of …

Simulated Annealing Approach To Flow Shop Scheduling, Sadhana Yellanki

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Flow Shop Scheduling refers to the process of allotting various jobs to the machines given, such that every job starts to process on a machine n only after it has finished processing on machine n-1, with each job having n operations to be performed one per machine. To find a schedule that leads to the optimal utilization of resources, expects the schedule to finish in a minimum span of time, and also satisfy the optimality criterion set for the related scheduling problem is NP-Hard, if n > 2. In this thesis, we have developed an algorithm adopting a heuristic called Simulated …

A Survey Of Classical And Recent Results In Bin Packing Problem, Yoga Jaideep Darapuneni

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In the classical bin packing problem one receives a sequence of n items 1, 2,..., n with sizes s1, s2, . . . ,sn where each item has a fixed size in (0, 1]. One needs to find a partition of the items into sets of size1, called bins, so that the number of sets in the partition is minimized and the sum of the sizes of the pieces assigned to any bin does not exceed its capacity. This combinatorial optimization problem which is NP hard has many variants as well as online and offline versions of the problem. Though …

Zero-Sum Magic Graphs And Their Null Sets, Samuel M. Hansen

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For any element h of the Natural numbers, a graph G=(V,E), with vertex set V and edge set E, is said to be h-magic if there exists a labeling of the edge set E, using the integer group mod h such that the induced vertex labeling, the sum of all edges incident to a vertex, is a constant map. When this constant is 0 we call G a zero-sum h-magic graph. The null set of G is the set of all natural numbers h for which G admits a zero-sum h-magic labeling. A graph G is said to be uniformly …