Graph Theory: An Algorithmic Approach

1976 ◽  
Vol 27 (4) ◽  
pp. 1027
Author(s):  
E. Kay ◽  
N. Christofides
Keyword(s):  
Graph Theory ◽  
Algorithmic Approach

scholarly journals Teaching Combinatorial Principles Using Relations through the Placemat Method

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1825
Author(s):  
Viliam Ďuriš ◽  
Gabriela Pavlovičová ◽  
Dalibor Gonda ◽  
Anna Tirpáková
Keyword(s):  
Graph Theory ◽  
Complexity Theory ◽  
Slovak Republic ◽  
Teaching Mathematics ◽  
Combinatorial Structures ◽  
Algorithmic Approach ◽  
Scientific Disciplines ◽  
Combinatorial Principles ◽  
The Subject ◽  
As Graph

The presented paper is devoted to an innovative way of teaching mathematics, specifically the subject combinatorics in high schools. This is because combinatorics is closely connected with the beginnings of informatics and several other scientific disciplines such as graph theory and complexity theory. It is important in solving many practical tasks that require the compilation of an object with certain properties, proves the existence or non-existence of some properties, or specifies the number of objects of certain properties. This paper examines the basic combinatorial structures and presents their use and learning using relations through the Placemat method in teaching process. The effectiveness of the presented innovative way of teaching combinatorics was also verified experimentally at a selected high school in the Slovak Republic. Our experiment has confirmed that teaching combinatorics through relationships among talented children in mathematics is more effective than teaching by a standard algorithmic approach.

scholarly journals The Fan–Raspaud conjecture: A randomized algorithmic approach and application to the pair assignment problem in cubic networks

2012 ◽  
Vol 22 (3) ◽  
pp. 765-778
Author(s):  
Piotr Formanowicz ◽  
Krzysztof Tanaś
Keyword(s):  
Graph Theory ◽  
Computer Networks ◽  
Assignment Problem ◽  
Perfect Matchings ◽  
Cubic Graphs ◽  
Cubic Graph ◽  
Algorithmic Approach ◽  
Edge Colorings ◽  
Mathematical Properties

Abstract It was conjectured by Fan and Raspaud (1994) that every bridgeless cubic graph contains three perfect matchings such that every edge belongs to at most two of them. We show a randomized algorithmic way of finding Fan–Raspaud colorings of a given cubic graph and, analyzing the computer results, we try to find and describe the Fan–Raspaud colorings for some selected classes of cubic graphs. The presented algorithms can then be applied to the pair assignment problem in cubic computer networks. Another possible application of the algorithms is that of being a tool for mathematicians working in the field of cubic graph theory, for discovering edge colorings with certain mathematical properties and formulating new conjectures related to the Fan–Raspaud conjecture.

scholarly journals An Algorithmic Approach to Wireless Sensor Networks Localization Using Rigid Graphs

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Shamantha Rai B ◽  
Shirshu Varma
Keyword(s):  
Wireless Sensor Networks ◽  
Graph Theory ◽  
Wireless Sensor Network ◽  
Sensor Networks ◽  
Computational Complexity ◽  
Path Loss ◽  
Wireless Sensor ◽  
Distance Information ◽  
Algorithmic Approach ◽  
Network Nodes

In this work estimating the position coordinates of Wireless Sensor Network nodes using the concept of rigid graphs is carried out in detail. The range based localization approaches use the distance information measured by the RSSI, which is prone to noise, due to effects of path loss, shadowing, and so forth. In this work, both the distance and the bearing information are used for localization using the trilateration technique. Rigid graph theory is employed to analyze the localizability, that is, whether the nodes of the WSN are uniquely localized. The WSN graph is divided into rigid patches by varying appropriately the communication power range of the WSN nodes and then localizing the patches by trilateration. The main advantage of localizing the network using rigid graph approach is that it overcomes the effect of noisy perturbed distance. Our approach gives a better performance compared to robust quads in terms of percentage of localizable nodes and computational complexity.

scholarly journals Chemical Formula Encryption - using Hamiltonian Circuits and Graph Valued Functions

2019 ◽  
Vol 8 (12) ◽  
pp. 4843-4846
Keyword(s):  
Graph Theory ◽  
Line Graphs ◽  
Chemical Formula ◽  
Hamiltonian Graphs ◽  
Algorithmic Approach ◽  
Practical Applications ◽  
Convenient Tool ◽  
Wide Range ◽  
Encryption And Decryption ◽  
Hamiltonian Circuits

The ever expanding nature of graph theory has made it a convenient tool for a wide range of practical applications. This study prescribes an algorithmic approach of cryptographic decoding of chemical formula using Jump graphs and Line graphs. Hamiltonian graphs are used as the key for encryption and decryption.

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