Sharif Digital Repository

The reconstruction conjecture is an open and interesting problem that attracts some reserchers. Although some work toward this problem has been done; but no one have been able to solve it comlpetely. In this thesis, some new theorms are developed which extend the domain of reconstructible graphs. Also, a generalization of graph spectrum -called Alpha Spectrum- is introduced that is very effective in recognization of graphs  

In 1953, Landau expressed the conditions for the existence of tournaments with a prescribed score vector R. Eleven years later, Ryser proposed an algorithm for constructing the tournament matrix with score vector R and showed that any two tournaments with the same score vector can be obtained from one another by a sequence of 3-cycle switches. Last year (2014) Brualdi and Fristcher explained in an article, similar to this process, the existence of, algorithm and switches for loopy tournament and Hankel tournament and similar structure skew-Hankel tournament. This paper is discussed in a chapter of this thesis. In 1991, De Caen found a lower bound for the real rank of a tournament matrix.... 

The so-called intersection problem has been considered for many different combinatorial structures, including Latin squares. This intersection problem basically takes a pair of structures, with the same parameters and based on the same underlying set, and determines the possible number of common sub-objects (such as blocks, entries, etc.) which they may have. The intersection problem has also been extended from consideration of pairs of combinatorial structures to sets of three, or even sets of , where may be larger than 3. In this thesis, we study the related problem of determining, for all orders n, the set of integers k for which there exists = 4 Latin squares of order n having... 

Social networks play a fundamental role as a media for the spread of inuence among its members. How people like to adopt innovation from their friends is known as word-of-mouth eect and has a long history of study in social science and recently in computer science and mathematics. In this context, The Inuence Maximization Problem is about nding initial active set of specic size in order to maximize the nal adoptions in the network through diusion of inuence. The optimization problem of the most inuential nodes selection is NPhard. As a result, some heuristic algorithms are needed to approximate the nal result. In this thesis some new heuristic algorithms were proposed with respect to... 

Gravitational lensing affects not only the position and number of images of cosmic objects but also their shapes. In the so-called weak gravitational lensing effects related to shape of the cosmic objects are studied. These require high quality images and wide field of view. Because of technology development and production of multi-chip CCD cameras in recent decades, we are witnessing an increase in the number of projects using weak lensing techniques. Taking instrumental errors into account, the first step in weak lensing studies should be the proper data reduction to produce final images in which instrumental errors are removed and have sufficient precision to be processed. In This thesis... 

Nowadays, because of drastically decrease of copper sulfide ore’s grade, and difficulties in leaching of them, new processes of copper production like bioleaching technique become significant. Finding the optimal conditions for bioleaching, require investing a lot of time and cost. Computer simulation is useful in this case. Temperature, affects the kinetics of dissolution reactions, type and growth rate of bacteria, and finally, rate and amount of recovery of valuable copper metal from ores, so determination of temperature within the bioheap is very important. Thermophiles are better than mesophiles in chalcopyrite bioleaching and in the range of 55 to 65 degree centigrade, thermophiles... 

There are many ways to color the vertices and edges of graphs, such as, rainbow connection, vertex coloring and dynamic coloring. In this thesis, in Chapter 1 we introduce a new coloring, we consider its relationship with some other colorings and we investigate its computational complexity. In chapter 1, we focus on the proper orientation number. The problem of orienting the edges of a given simple graph so that the maximum indegree of vertices is minimized was introduced in 2004. We show that there is a polynomial time algorithm for determining the proper orientation number of a given 3-regular graph. But it is NP-complete to decide if the proper orientation number of a 4-regular graph is 3... 

A Latin square of order n, is an n n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column.Two cells of a Latin square are independent when they are not in the same row, or in the same column and they are not the same symbol. If they are not independent, they are called dependent. A k-coloring of a Latin square is assigning k colors to its cells where no two dependent cells have the same color. The smallest k for which we have a k-coloring for a Latin square L with k colors is called chromatic number of L and we denote it by L). If we consider the Cayley table of an arbitrary finite group of order n, then we have a Latin square of... 

Finding necessary and sufficient conditions for a sequence to be graphic or in more general setting existence of factor with predscribed degree sequence of a general graph and also existence of a polynomial algorithm for finding this factor are classical problems of graph theory. These problems were discussed and solved between 1952 to 1972 by prominent mathematicians such as Erdős, Tutte, Edmonds et al. In this thesis we initially discuss most generalized forms of this problems namely Tutte’s f-factor and Lovasz’ (g; f)-factor theorems. Then some simple generalization of the special cases like Erdős-Gallai and Gale-Ryser theorems are investigated. And by using a form of Lovasz’ (g;... 

Decomposition of a graph into it’s subgraphs is an important problem in Graph Theory and Combinatorics. In this thesis we investigate some papers and their results about the problem of the decomposition of a complete graph into 4−cycles. In chapter 1 we express some parts of a paper written by Bryant, Darryn, Horsley, Daniel, and Pettersson. After giving some definitions and notations about cycle systems and their spectrums, we use methods of the paper to give a proof for a theorem on the existence of a decomposition of complete graphs into 4−cycles. In the next three chapters we explain results of a paper written by Bryant, Darryn, Grannell, Mike, Griggs, Terry, and Mačaj, Martin. chapter 2... 

Sudoku is an intellectual game based on mathematics. Sudoku achieved global fame in a short time because this game doesn’t need any mathematical operation like addition and multiplication and in theory, instead of numbers, lechers, shapes,colors, etc. could be placed.Sudoku which is a single-player game in generally the player should complete a partial n2 × n2 matrix M all of whose enteries are drawn from {1; 2,..., n2} by applying the rules: no number may appear more than once in any row, any column,or any of the nine ‘‘blocks’’. Actually blocks are n × n submatrixs with indices {na + 1, na + 2,…, na + n} × {nb + 1, nb + 2,….., nb + n} Actually, A Sudoku is A Latin square with one... 

The concept of defining set in matching theory, recently has been taken into consideration by chemists and mathematicians because of several important applied problems in chemistry and mathematics. This concept is studied extensively in vari-ous areas of combinatorics and graph theory. The idea is to obtain total combinatorial structure of one object uniquely, based on some special information about it. Defin-ing set has been studied in various areas of graph theory like colouring, matching , orientations of graphs and etc. and many researches have been done in these areas. What we focus on, in this thesis is the defining set in matching theory that has been called “forcing set”. A minimum... 

Due to the increasing number of research activities across the world,the academic societies are in the urgent need of appropriate criteria and methods for the evaluation of scientific publications. The term ‘Scientometrics’ has been coined to describe the methodology of aforementioned scientific assessment. Introduction of comprehensive and universal scientific rankings could provide inexperienced researchers with the opportunity to select most qualified publications for their literature reviews on the basis of such rankings. This procedure seems to be more convenient and reliable.In this framework, a review of most commonly used scientometric principles and methods are presented in the... 

One of the fields, in which graph theory and computer science have been appleid,is architectural design. Some of these applications are presented in this thesis. This thesis has two parts, the first part peresents a systematic pathway for design of a floor plan when given the list of cells, the required dimensions of each cell and the matrix of required adjacencies between the cells. (Based on the article by Hashimshony(1988)) The second part is about the application of Evolutionary Algorithm (EA) in ar-chitucture. The architectural layout design problems, which is concerned with the finding of the best adjacencies between functional spaces among many possible ones under given constraints,... 

The Sudoku puzzle is played on a 9 × 9 grid which is divided into nine boxes each with 3 × 3 cells. Initially, some digits between 1 and 9 are given on the grid as the clues. Generalized Sudoku (a table of n2 by n2 that includes n2 blocks with n cells and in each of its rows, columns and blocks has all numbers from 1 to n2 appeared once and only once) can be considered too. Millions of people around the world are tackling one of the hardest problems in computer science without even knowing it. The first such puzzle appeared in the May 1979 edition of Dell P encil P uzzles and W ord Games and, according to research done by W ill Shortz, the crossword editor of the N ew Y ork T imes, was...