Free

# Graph theory - Research Paper Example

Summary
The concept of graph theory begun in problems pertained to recreational Mathematics. However, as noted by Biggs (122), it has developed into an essential…

## Extract of sample "Graph theory"

Graph Theory Introduction Graph theory refers to a branch of Mathematics that deals with a network of points that are connected by lines (Biggs 122). The concept of graph theory begun in problems pertained to recreational Mathematics. However, as noted by Biggs (122), it has developed into an essential area of mathematical research with several applications in physical, biological, and natural sciences. Importantly computer science essentially depends on concepts of graph theory. The historical development of graph theory can traced back to the year 1735, when Leonhard Euler a Swiss Mathematician developed a solution to an old puzzle related to the possibility of establishing a path across every one of the seven bridges that span a forked river flowing past (Biggs 140). From a conceptual perspective, a graph is formed by vertices and edges linking the vertices. From a formal perspective however, a graph refers to a pair of sets (V, E), where V is a set of vertices and E is a set of edges. Based on these fundamental concepts underpinning graph theory, this paper seeks to explain the importance and application of the theory’s theoretical concepts in various fields (Biggs 124).
The concept of graph theory is important because graphs allow for a simplification of complex concepts, eliminating the irrelevant details without forfeiting much information necessary for the task. As asserted by Biggs (148), the assumptions made by the graph theory match the real world conditions and are therefore not comparable to any other model. Among the fundamental uses of the graph theory entail; giving a unified formalism for diverse looking real life problems. This has been the sufficient basis upon which algorithms have been presented in this common formalism.
The theoretical concepts underpinning graph theory are widely used in the studying and modeling of various applications, in diverse fields. These include; construction of bonds in chemistry, study of molecules, and the study of atoms. Graph theory is widely used in Sociology for instance to measure the prestige of actors or in exploring the mechanisms of diffusion (Biggs 150). Besides, the conservation efforts made in biological sciences essentially apply the concepts of graph theory where a vertex represent regions where certain species exist and the edges are used to represent paths of migration or movement from one region to another (Biggs 152). Such information is important more so when examining the breeding patterns or tracking the spread of parasites, diseases and in the study of the consequences of migration that affect other species. Theoretical concepts of graph theory are widely used in the field of operations research. For instance, the common travelling salesman problem, the short spanning tree in a weighted graph, obtaining the favorable match of jobs and men and establishing the shortest path between two vertices in a graph. The network activity which primarily employs concepts of graph theory is used in solving complex numbers of combinatorial problems. The most successful and common application is the planning and scheduling of large complex projects. In such a project, edges represent the moves and vertices represent the positions.
Conclusion Concisely, it is not possible to estimate the necessity of concepts of graph theory in contemporary Mathematics. Elegant and deep in itself, graph theory entail a considerable number of wonderful results and ideas that are essential in various fields of Mathematics. As illustrated in this paper, the theoretical underpinnings of the graph theory provide the theoretical basis for developing important concepts in applied fields such as; operations research, computer science, management science, mechanical and electrical engineering.
Work Cited:
Biggs, Wilson. Graph Theory. New York: Clarendon Press, 1986. Print. Read More
Cite this document
• APA
• MLA
• CHICAGO
(“Graph theory Research Paper Example | Topics and Well Written Essays - 500 words”, n.d.)
Graph theory Research Paper Example | Topics and Well Written Essays - 500 words. Retrieved from https://studentshare.org/miscellaneous/1596176-graph-theory
(Graph Theory Research Paper Example | Topics and Well Written Essays - 500 Words)
Graph Theory Research Paper Example | Topics and Well Written Essays - 500 Words. https://studentshare.org/miscellaneous/1596176-graph-theory.
“Graph Theory Research Paper Example | Topics and Well Written Essays - 500 Words”, n.d. https://studentshare.org/miscellaneous/1596176-graph-theory.
Click to create a comment or rate a document

## CHECK THESE SAMPLES OF Graph theory

### Theory

... Module: Democracy as an End in Itself or a Means to an End There has been a belief that majority of thewestern nations achieved prosperity due to their advancement in democracy. Advocates of democracy have been fighting against socialism and communism for over 200 years but since the World War II democracy started to gain root in many countries especially in the east. The Cold War marked quite a significant period where democracy emerged a victor over communism. Using this analysis democracy acts as an end to countries that have been undergoing turmoil or other instabilities. Other outlooks bring forth the concept that democracy is a means to an end. In considering each claim it is important to look into what democracy actually... Module:...
4 Pages(1000 words)Term Paper

### The Development of Cancer Problem: 1998-2008

10 Pages(2500 words)Article

### Graph theory Applications in Computer programming

...? Graph theory Applications in Computer programming Two applications of Graph theory in Computer programming In computing, programs are designed to successfully handle large graphs that are encountered in form of networks such as transportation networks, electrical networks, flow networks, and PERT among others (Kasyanov & Evstigneev, 1994). It is important to understand that manipulating and analyzing graphs and sub-graphs is nonnumeric which means that the programs involve strong ability make decisions. One application of graph theory in programming is in algorithms. According to Deo (1974, p. 284), Computer algorithms are essential sets of instructions pursued to resolve certain problems. The implication is that every step... of an...
3 Pages(750 words)Essay

### Economics Indicator Paper and Graph

...rates have declines from 1999 until 2004 where interest rates have risen to date, interest rates are the cost of borrowing funds and therefore with the increase in interest rates means that les houses are built or the demand for houses has declined as the cost of funds increase with interest rates. Keynes theory and interest rates: Keynes emphasised the importance of the level of interest rates on investment levels, according to Keynes when interest rates were high then the level of cost of funds was high and the level of investment would be low, if interest rates declined then the level of investment would rise, therefore according to Keynes the interest rate investment relationship can be simplified in the following...
2 Pages(500 words)Essay

### Graph key features of functions, linear equations and linear inequalities

...one-to-one or many-to-one correspondence between the values of ‘x’ in the domain and the matching values of ‘y’ in the range. Given a set of ordered pairs that define a function, each element ‘x’ in the domain is distinct and does not repeat in value when paired with an element ‘y’ in the range. Through a vertical line test, one may determine whether or not a relation is a function in a graph such that on running down a vertical line, the curve is hit only at a single point everywhere in the curve. In this manner, it may be claimed that a ‘linear equation’ is a function, but not all functions are linear in nature. Examples of a Function: (a) A Set of Ordered Pairs: {(-7, 4) , (-3, 0) , (1, 5) , (2, -2) , (6,...
2 Pages(500 words)Essay

### Frequency Distribution Graph

...Frequency Distribution Graph Without a doubt, histogram plays a critical role in portraying calculated  grouped frequency distribution based on both dependent and independent variable within interval or ratio level of measurement. More significantly, it consists of vertical bars that are drawn above scores intervals. As a result, either it can make the height of the bar correspond with the frequency or width of the bar broadens to the actual limits of the score interval. Considerably, descriptive statistics is essential with describing the relationship between variables by summarizing large amount of data. More so, descriptive statistics establishes the mean, mode and median central tendency useful in measure of...
5 Pages(1250 words)Statistics Project

### Curve Graph - numbers included

.... of coffee and 12 lbs. of nuts ii. This is efficient g. Is the point at 24 pounds of coffee per day, 24 pounds of nuts per day an attainable point? Is it an efficient point? i. Yes it is attainable 1. Susan = 24 lbs. of coffee 2. Tom = 24 lbs. of nuts ii. This is efficient h. On a graph with pounds of coffee per day on the vertical axis and pounds of nut on the horizontal axis, show all the points you identified in parts a-g.... I do not know if this makes any difference, but I use a MAC computer Nancy and Bill are auto mechanics. Nancy takes 4 hours to replace a clutch and 2 hours to replace a set of brakes. Bill takes 6 hours to replace a clutch and 2 hours to replace a set of brakes. State whether anyone has an absolute advantage at...
1 Pages(250 words)Statistics Project

### Spectral graph theory

...Spectral Graph Theory The concept of graph theory has been used in variant areas of mathematics, science and technology which has been highly acknowledged over the years (Beineke, Lowell and Robin 66). This is evident as firms adopt the concept in fields such as biochemistry, computer science, and engineering and communication networks. This is without forgetting the wide use in computation and operations investigations by researcher and specialists (Cvetković & Dragoš, 7). The graph theory makes use of different techniques to prove basic results in important areas such as mathematics and science. In this paper I will examine the...
15 Pages(3750 words)Research Paper

### Questions and comments on graph and starbucks

... Euro’s Exchange Rate and Starbucks Question There are multiple reasons d for the rise in Euro’s exchange rate, which apart from Chinese foreign reserves diversification intent include large inflows of capital in European markets and shrinkage of the balance sheet of European Commercial Bank (ECB). China, however, presents an even bigger challenge towards Euro’s continuing strengthening. The stance of Chinese government to diversify its foreign reserves can considerably increase the value of Euro in comparison with other currencies, and most importantly US dollar too. Moreover, a stronger Euro will definitely make it difficult for European economies to compete in the global market due to comparatively low prices offered by non... Euro’s...
1 Pages(250 words)Essay

### Applications of Graph Theory

...Graph theory in Networking Affiliation Graph theory in networking Graph theory is one of the most applied mathematical theories in the various fields. It is also referred to as the study of graphs. It is a mathematical branch that focuses on encoding networks and measurement of network properties (Mandal et al., 2012). A graph refers to a set of edges and vertices where a pair of vertices is connected by an edge. The graph theory originated in 1735, as Euler attempted to solve the Koinsberg bridge problem and later constructed a graphical structure known...
4 Pages(1000 words)Assignment