# Discussion On Graph Labeling in Graph Theory

Categories: Data Analysis

## Applications of Graph Labeling in Major Areas of Computer Science

### Introduction

G is called a labeled graph if each edge e=uv is given the value f (uv) = f (u)*f (v), where * is a binary operation. In literature * can be represented as either of addition, multiplication, modulo addition or subtraction, absolute difference or symmetric difference [26].

### Problems with graph labeling? Most of the graph labeling problems have three ingredients:

1. A set of numbers S from which the labels are chosen:
2. A rule that assigns a value to each edge:
3. A condition that these values must satisfy.

In graph theory, graph labeling plays a vital role by using graph labeling; we can easily understand the graph. Structure mining or structured data mining is the process of finding and extracting useful information from semi structured sets of data. Graph mining is a special case of structured data mining. In data mining graphs can be more widely used because the outputs of data mining can be represented in graphs.

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Networks representation plays an important role in many domains of computer science, ranging from data structures and graph algorithms, to parallel and distributed computing, and communication networks.

Now a day’s database management is most efficiently used in many applications. In this data exists in the tables can be taken as nodes and then draw connections between the nodes what type of relationship exists can be taken as labeling in nodes.

Encryption has fascinated extra responsiveness owing to the swift development in multimedia and network technologies where the data can be shielded from unauthorized access.

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Image scrambling is a scheme that provides protection for digital images. The results point out that the new image scrambling method established on graceful labeling of tree can deliver a high level secure owing to the strong anomaly of sorting transformation.

The concept of public key cryptography proved extremely useful to solve problems coming up with the possibilities of the Internet and it is realized not only secure communication but for example digital signatures or digital authentication protocols as well.

Connected components labeling scans an image and groups its pixels into components based on pixel connectivity means all pixels in a connected component share similar pixel intensity value and are in some way connected with each other. Once all the groups have been determined, each and every pixel is labeled with a gray level or a color (color labeling) according to the component it was assigned to extracting and labeling of various disjoint and connected components in an image is central to many automated image analysis applications.

Labeling of a binary image is the operation of assigning a unique value to each pixel belonging to the same region of the connected pixels. The results can be obtained and these are different. Security labels convey information used by protocol entities to determine how to handle data communicated between open systems. Information on a security label has been used to control access, specified protective measures, and determined additional handling restrictions required by a communications security policy.

In communication networks also it is applied because the route establishment, allocation of channels, security also provided in the networks.

The odd graceful labeling is one of the most widely used labeling methods of graphs [27] .While the labeling of graphs is perceived to be a primary theoretical subject in the field of graph theory and it serves as models in a wide range of applications.

### Role of Graph Labeling:

#### Get Another Label? Improving Data Quality and Data Mining Using Multiple, Noisy Labelers

This addresses the repeated acquisition of labels for data items when the labeling is imperfect. We examine the improvement (or lack thereof) in quality of data via repeated labeling, and focus especially on the improvement of training labels for supervised induction. With the outsourcing of small tasks becoming easier, for example, via Rent-A-Coder or Amazon’s Mechanical Turk, it is often possible to obtain less-than-expert labeling at low cost. With low-cost labeling, preparing the unlabeled data part can become considerably more expensive than labeling.

We present repeated-labeling strategies of increasing complexity, and show several main results.

1. Repeated-labeling can improve label quality and model quality, but not always.
2. When labels are noisy, repeated labeling can be preferable to single labeling even in the traditional setting where labels are not particularly cheap.
3. As soon as the cost of processing the unlabeled data is not free, even the simple strategy of labeling everything multiple times can give considerable advantage.
4. Repeatedly labeling a carefully chosen set of points is generally preferable, and we present a robust technique that combines different notions of uncertainty to select data points for which quality should be improved. The bottom line: the results show clearly that when labeling is not perfect, selective acquisition of multiple labels is a strategy that data miners should have in their repertoire; for certain label quality or cost regimes, the benefit is substantial.

### Standard Security Label for Information Transfer

Information Transfer security labels convey information used by protocol entities to determine how to handle data communicated between open systems. Information on a security label can be used to control access, specify protective measures, and determine handling restrictions required by a communications security policy.

Security label -A marking bound to a resource (which may be a data unit) that names or designates the security attributes of that resource.

### Explanation:

Security labels convey information used by protocol entities to determine how to handle data communicated between open systems. Information on a security label can be used to control access, specify protective measures, and determine additional handling restrictions required by a communications security policy.

This standard defines security label syntax for information exchanged over data networks and provides label encodings for use at the Application and Network Layers. The syntactic constructs defined in this standard are intended to be used along with semantics provided by the authority establishing the security policy for the protection of the information exchanged.

The label presented here defines security tags that may be combined into tag sets to carry security related information. Five basic security tag types allow security information to be represented as bitmaps, attribute enumerations, attribute range selections, hierarchical security levels, or as user-defined data.

Because of inherent differences in layer functionality, the security label defined in this document is expressed both as an abstract label syntax specification for the OSI Application Layer and an encoding optimized for use at the Network Layer.

### Dynamic Security Labels and Noninterference

Information flow control protects information security by constraining how information is transmitted between objects and users of various security classes. These security classes are expressed as labels associated with the information or its containers.

We propose an expressive language based mechanism for securely manipulating information with dynamic security labels. The mechanism is formalized in a core language (based on the typed lambda calculus) with first class label values, dependent security types and run time label tests.

Further, we prove that any well typed program of the core language is secure because it satisfies noninterference.

For example, a file has associated access permissions that cannot be known with certainty until it is opened. Although one security typed programming language has included support for dynamic security labels, there has been no demonstration that a general mechanism for dynamic labels can securely control information flow. In this paper, we present an expressive language based mechanism for reasoning about dynamic security labels. The mechanism is formally presented in a core language based on the typed lambda calculus; any well typed program in this language is provably secure because it satisfies noninterference.

### Graph Labeling in various types of communication networks:

Traditional network representations are usually global in nature. That is, in order to retrieve useful information, one must access a global data structure representing the entire network. Massive graphs are everywhere, from social and communication networks to the

### World Wide Web

The geometric representation of the graph structure imposed on these data sets provides a powerful aid to visualizing and understanding the data.

In sensor networks, it provides fast communication with the help of radio labeling. Here each vertex represents a transmitter and any pair of vertices connected through an edge corresponds to neighboring transmitters. Here the kind of labeling used is Radio labeling which is defined as Let G = (V (G), E (G)) be a connected graph and let d (u, v) denote the distance between any two vertices in G.

Automatic channel allocation is also possible in wireless networks why because to find an efficient way, safe transmissions are needed in areas such as Cellular telephony, Wi-Fi, Security systems and many more. If more than one candidate vertex is available, then the final selection is replaced by a deterministic selection function to select the vertex. The protocol operation is done by identifying the neighbors by means of hearing the messages generated by the access points.

In social networks, it is most efficient and provides effective communication. It provides effective communication by using certificates and key graphs. An important contribution to social network analysis came from sociograms. A sociogram can be seen as a graphical representation of a network: people are represented by dots (called vertices) and their relationships by lines connecting those dots (called edges).

These are some types of graph labeling that plays a role and it has other types also like adhoc networks, sensor networks, compression networks etc…

### Software Configuration Management

Label with the test-ready tag when a new (updated respectively) revision of a file is checked in into VS (it’s the latest revision at a moment in fact; but this would not be necessarily fulfilled in the future that’s the reason why we need a ‘checkpoint’, technically speaking a label). Label with ‘release’ tag when a new release is being built.

Basically there are two kinds of a label to consider. From the developer’s side, it is the test ready label (e.g. testready). Release manager takes care of the release label (e.g. v1.1.010).

### Who is applying the label?

The test-ready label is to be applied by a developer. In case of consistency fix the label can be applied (moved) by the release manager. The release label is to be applied by a release manager only. No developer is allowed to interact with the release label(s) in any way to preserve the consistent state. During the first phase of a development project, there are just unit tests in the place and no software releases, thus labeling is needed just later on.

The trigger to start labeling is the request of very first project version release, commonly prior to first test phase, e.g. before FAT13.

‘Code freeze’14time-line has to be introduced in 10 technically would not be possible to store exactly in the form of ‘v1.1.0’ for instance; if so, common labels look like ‘V1_1_0’ instead.

Then finally applied the labeling methodology enforces once to move of the release label the promotion of the new release.

The time-based checkpoint all software revisions are considered as test-ready, i.e. labeled with test-ready label. For purposes of the very first release all files with test-ready label are labeled with the release tag.

FAT ~ Factory Assembly Test; single module of system included to project is being tested without interconnectivity nor interaction with other modules or systems; maximally the stubs are used ‘code freeze' is an expression for disallowance of another code commits to versioning system; a need for this pops up when the first release related labels, are going to be applied (test-ready and release label, e.g. v1.0.0);

Because there was no test-ready revision so far, the one delivered at ‘code freeze’ time is the one labeling has been applied for the very first time. There is no other release label except initial version and test-ready label, both pointing to the same revision of a single file.

### Graph theory in symbol recognition:

Here, the authors have discussed the paper “Symbol Recognition by Error tolerant sub graph matching between region adjacency graphs” (The region adjacency graph is one which costs are associated with both nodes and arcs, implying that an update of these costs must be included in the given algorithm as node costs change due to the connecting two regions Ri and Rj. The graphs shown below are the segmented graph, the region adjacency graphs and its dual graph respectively).

The distorted image sub graph is matched with the model graph. That is the image region and the model regions are modeled as the image sub graph and model graph. The cost of adding a neighbor to the correspondence is the cost of the string edit distance aligning the polygonal approximated outer boundaries of the graphs consisting of the matched regions and the neighbor region candidates. This method is applicable to any region adjacency graph representation.

### A Simple and Efficient Connected Components Labeling Algorithm

We describe a two-scan algorithm for labeling connected components in binary images in raster format. Unlike the classical two-scan approach, our algorithm process equivalences during the first scan by merging equivalence classes as soon as a new equivalence is found. We show that this significantly improves the efficiency of the labeling Process with respect to the classical approach. The data structure used to support the handling of equivalences is a 1D-array.

In our labeling algorithm equivalences are processed directly in the first scan so that equivalence classes are always maintained updated during the scan. This is obtained by associating a new equivalence class with each new label and by merging the corresponding classes as soon as a new equivalence is found.

We perform the merging operation using a very simple data structure called Class Array (C). C is a one dimensional array as large as the maximum label value and continuing for each label value its corresponding class identifier.

### Information Security Classification Guidelines

If information is not classified, program areas may apply either overly expensive controls unnecessarily or inappropriately weak controls. It may result in the waste of resources or high risk of information misuse, loss or disclosure.

Information security classification enables the selection and implementation of adequate security controls.

As defined in the information security classification standard, there are three information security classification levels: High, Medium and Low. These security levels are consistent with risk classifications used in other areas of government.

For each classification level, a detailed description is provided to describe the potential level of risk or harm in the financial, personal, and operational aspects. Once information is classified, the information needs to be labeled. Labels are linked to an associated classification level. Information at the same level can be labeled differently since they need to be handled differently though they are protected with the same level of protection measures.

For example, Cabinet Confidential information and High Sensitivity information will receive the same level of protection, but they will be handled differently due to business processes and handling requirements.

### Conclusion

The main aim of this paper is to explore the role of Graph Labeling in Computer science field. Graph Labeling is a powerful tool that makes things ease in various fields of computer science as said above. An overview is presented especially to project the idea of Graph Labeling. Researchers may get some information related to graph labeling and its applications in computer science field and can get some ideas related to their field of research.

Updated: Feb 13, 2024