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... 

Partial Differential Equations (PDEs) play a crucial role in modeling various physical, biological, and engineering phenomena. One of the most important and complex of these equations is the Monge-Ampère equation, which appears in various fields including differential geometry and optimization theory. In this thesis, after defining and examining the preliminary properties of the Monge-Ampère measure and defining the Alexandrov weak solution, the existence and uniqueness of this weak solution for the Dirichlet problem are addressed, and finally, the regularity problem is studied  

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... 

In the process of gene assembling, the molecular structure of a DNA chain, can be modeled by a signed graph. After that by means of a composition of three reduction rules: gnr, gpr and gdr, that is called reduction strategy, this graph is reduced to a null graph. If the composition of any ordering of rules in a reduction strategy such as S, is applicable on a signed graph G, then we say that S can be applied in parallel to G and the set S is said to be a parallel step for reduction of that graph. Also we define the least number of parallel steps in reduction of a graph, to be the parallel complexity of that graph, and denote it C(G). In this thesis, a collection of particular signed graphs,... 

There is much interest in the theoretical study of the structure of hypercubes because their structure has played an important role in the development of parallel processing and is still quite popular and influential.This thesis will begin with an introduction to hypercubes and some of their problems. Then we study the following concepts: Arboricity (The minimum number of edge-disjoint forests into which a graph can be decomposed), Galactic number (similar to arboricity but such that each component of each forest is a star), Silver coloring (Given a set I of maximal independent vertices, a silver coloring with respect to I is such that every v 2 I sees every other colors in its closed... 

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,... 

Since critical and defining sets have been examined in various fields of combinatorics, including Latin squares and different branches of graph theory, we aim to present a portion of the obtained results con-cerning defining sets in diverse fields of graph theory, and provide a survey on them.In the present dissertation, we examine defining sets of vertex coloring,edge coloring, total coloring and forcing sets of orientation of graphs,perfect matching, hull and geodetic sets. Since complete graphs’ col-oring defining sets and Latin squares’ critical sets are closely related,we shall discuss them in a coloring framework. Furthermore, for dif-ferent graph families, including regular graphs,... 

Since today graphs have many applications in different sciences including computer networks, in this thesis a number of graphs which have been widely used in computer networks, are studied.The graphs presented in this thesis are hypercubes, generalized hypercubes (Bhuyan and grawal, 1984), balanced hypercubes (Huang and Jie, 1992) and the star graphs (Sheldon and Akers, 1987), which are the generalization of the hypercubes and have similar properties.In general the graph which is considered for computer networks as an interconnection structure,should have small degrees of vertices, a small diameter, and a large number of paths between any two vertices. Thus in our studies these three...