# The Fascinating World of Graph Theory

@inproceedings{Benjamin2015TheFW, title={The Fascinating World of Graph Theory}, author={Arthur T. Benjamin and Gary Chartrand and Ping Zhang}, year={2015} }

The fascinating world of graph theory goes back several centuries and revolves around the study of graphsmathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematicsand some of its most famous problems. For example, what is the shortest route for a traveling salesman seeking to visit a number of cities in one trip? What is the least…

## Topics from this paper

## 32 Citations

HAMILTONICITY OF CAMOUFLAGE GRAPHS

- Computer ScienceInternational Journal of Engineering Applied Sciences and Technology
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The result proved that “Every connected vertex-transitive simple graph has a Hamilton path” shows a significant improvement over the previous efforts by L.Babai and L.Lovasz.

On Eulerian Irregularity and Decompositions in Graphs

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For a nontrivial connected graph G of size m, it is shown that ( m+1 2 ) ≤ EI(G) ≤ 2 ( m+1 2 ) and that EI(G) = 2 ( m+1 2 ) if and only if G is a tree of size m. A necessary and sufficient condition…

Collatz Sequences in the Light of Graph Theory

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It is well known that the inverted Collatz sequence can be represented as a graph or a tree. Similarly, it is acknowledged that in order to prove the Collatz conjecture, one must demonstrate that…

Homometric Number of a Graph and Some Related Concepts

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- 2016

It is proved that the homometric number of the Cartesian product of two graphs is at least twice the product of the homomet numbers of the individual graphs.

Business Network Analytics: From Graphs to Supernetworks

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This chapter discusses issues related to the computational complexity of some problems associated with data analytics and provides a survey on recent applications and new algorithmic approaches for data analytics.

A BIPARTITE GRAPH ASSOCIATED WITH IRREDUCIBLE ELEMENTS AND GROUP OF UNITS IN Z n

- 2018

A nonzero nonunit a of a ring R is called an irreducible element if, for some b, c ∈ R, a = bc implies that either b or c (not both) is a unit. We construct a bipartite graph in which the union of…

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- 2018

A main tenet of this book is that the idea-structure for many puzzles typically originates in the imagination (a right-hemispheric function) and then migrates, via a cognitive flow, to embed itself…

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As argued throughout this book, puzzles have played as much a role as any other human artifact, mental tool, or device in human history as sparks for discovery. The Ahmes Papyrus is more than a…

Reviews

- Computer Science
- 2016

This note assumes that the definition of ‘fascinating’ is some convex combination of these qualities, and gives a proof of the following result.

Puzzles and Mathematics

- 2018

The English word puzzle covers a broad range of meanings, alluding to everything from riddles and crosswords to Sudoku, optical illusions, and difficult conundrums in advanced mathematics. As a…

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