Graph Theory, Coding Theory and Block Designs

1975 ◽  
Author(s):  
P. J. Cameron ◽  
J. H. van Lint
Keyword(s):  
Graph Theory ◽  
Coding Theory ◽  
Block Designs

Total Irregularity Strengths of an Arbitrary Disjoint Union of (3,6)- Fullerenes

2020 ◽  
Vol 23 ◽  
Author(s):  
Ayesha Shabbir ◽  
Muhammad Faisal Nadeem ◽  
Mohammad Ovais ◽  
Faraha Ashraf ◽  
Sumiya Nasir
Keyword(s):  
Graph Theory ◽  
Lower Bound ◽  
Coding Theory ◽  
Disjoint Union ◽  
Fullerene Molecule ◽  
Graph Labeling ◽  
Fullerene Graph ◽  
Theoretical Concepts ◽  
Large Numbers ◽  
Fullerene Graphs

Aims and Objective: A fullerene graph is a mathematical model of a fullerene molecule. A fullerene molecule or simply a fullerene is a polyhedral molecule made entirely of carbon atoms other than graphite and diamond. Chemical graph theory is a combination of chemistry and graph theory where graph theoretical concepts used to study physical properties of mathematically modeled chemical compounds. Graph labeling is a vital area of graph theory which has application not only within mathematics but also in computer science, coding theory, medicine, communication networking, chemistry and in many other fields. For example, in chemistry vertex labeling is being used in the constitution of valence isomers and transition labeling to study chemical reaction networks. Method and Results: In terms of graphs vertices represent atoms while edges stand for bonds between atoms. By tvs (tes) we mean the least positive integer for which a graph has a vertex (edge) irregular total labeling such that no two vertices (edges) have same weights. A (3,6)-fullerene graph is a non-classical fullerene whose faces are triangles and hexagons. Here, we study the total vertex (edge) irregularity strength of an arbitrary disjoint union of (3,6)-fullerene graphs and providing their exact values. Conclusion: The lower bound for tvs (tes) depending on the number of vertices, minimum and maximum degree of a graph exists in literature while to get different weights one can use sufficiently large numbers, but it is of no interest. Here, by proving that the lower bound is the upper bound we close the case for (3,6)-fullerene graphs.

scholarly journals Block designs and graph theory

1966 ◽  
Vol 1 (1) ◽  
pp. 132-148 ◽  
Author(s):  
Jane W. Di Paola
Keyword(s):  
Graph Theory ◽  
Block Designs

On the applications of Extremal Graph Theory to Coding Theory and Cryptography

2013 ◽  
Vol 43 ◽  
pp. 329-342 ◽  
Author(s):  
Monika Polak ◽  
Urszula Romańczuk ◽  
Vasyl Ustimenko ◽  
Aneta Wróblewska
Keyword(s):  
Graph Theory ◽  
Coding Theory ◽  
Extremal Graph ◽  
Extremal Graph Theory

Block Design Games

1961 ◽  
Vol 13 ◽  
pp. 110-128 ◽  
Author(s):  
A. J. Hoffman ◽  
Moses Richardson
Keyword(s):  
Linear Programming ◽  
Graph Theory ◽  
Network Flows ◽  
Automorphism Groups ◽  
Block Design ◽  
The Other ◽  
Block Designs ◽  
Simple Games ◽  
Extensive Family ◽  
Natural Way

In this paper, we define and begin the study of an extensive family of simple n-person games based in a natural way on block designs, and hitherto for the most part unexplored except for the finite projective games (13). They should serve at least as a proving ground for conjectures about simple games. It is shown that many of these games are not strong and that many do not possess main simple solutions. In other cases, it is shown that they have no equitable main simple solution, that is, one in which the main simple vector has equal components. On the other hand, the even-dimensional finite projective games PG(2s, pn) with s > 1 possess equitable main simple solutions, although they are not strong either. These results are obtained by means of the study of the possible blocking coalitions. Interpretations in terms of graph theory, network flows, and linear programming are discusssed, as well as k-stability, automorphism groups, and some unsolved problems.

scholarly journals Computing The Irregularity Strength of Planar Graphs

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 150 ◽  
Author(s):  
Hong Yang ◽  
Muhammad Siddiqui ◽  
Muhammad Ibrahim ◽  
Sarfraz Ahmad ◽  
Ali Ahmad
Keyword(s):  
Graph Theory ◽  
Circuit Design ◽  
Planar Graphs ◽  
Coding Theory ◽  
Vital Role ◽  
Graph Labeling ◽  
X Ray Crystallography ◽  
Radar Astronomy ◽  
Base Management ◽  
Irregularity Strength

The field of graph theory plays a vital role in various fields. One of the important areas in graph theory is graph labeling used in many applications such as coding theory, X-ray crystallography, radar, astronomy, circuit design, communication network addressing, and data base management. In this paper, we discuss the totally irregular total k labeling of three planar graphs. If such labeling exists for minimum value of a positive integer k, then this labeling is called totally irregular total k labeling and k is known as the total irregularity strength of a graph G. More preciously, we determine the exact value of the total irregularity strength of three planar graphs.

Combinatorics: A Very Short Introduction

2016 ◽  
Author(s):  
Robin Wilson
Keyword(s):  
Graph Theory ◽  
Latin Squares ◽  
Block Designs ◽  
Short Introduction ◽  
Computer Theory ◽  
Minimum Number ◽  
As Graph

Combinatorics is the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics such as graph theory, partitions of numbers, block designs, design of codes, and latin squares. Combinatorics: A Very Short Introduction provides an overview of the field and its applications in mathematics and computer theory, considering problems from the shortest routes covering certain stops to the minimum number of colours needed to draw a map with different colours for neighbouring countries.

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