Perhaps the most common graph theory problem is that of the Travelling Salesman Problem (TSP), which is somewhat like Euler’s original seven bridge problem, but instead asks for a traveller (a ...

Graph polynomials ... of the Euler-genus polynomial, a critical tool in classifying topological graph embeddings [2]. In addition, recent research in matroid theory has harnessed linear algebraic ...

For decades, engineers have utilized Petri nets to develop automated systems with specific functional requirements or ...

Euler’s paper arguably marks the beginning of topology and graph theory. Even the paper’s title shows that Euler himself was aware that he was dealing with a new type of geometry in which ...

This argument is considered the first result in graph theory, and paths through graphs that visit every edge once are now called Eulerian paths. Technically Euler’s argument describes only the ...

This approach echoes the pioneering spirit of Leonard Euler, Father of graph theory whose “Seven Bridges of Königsberg” problem introduced foundational principles in the field. By conceptualizing ...

This is the case with an important problem in computer science called "graph isomorphism testing" whereby scientists use ...

Euler considered graphs for which there exists a path between every two nodes (called connected graphs). He proved that a connected graph with undirected edges contains an Eulerian cycle exactly ...

Agnes M. Herzberg and M. Ram Murty of Queen’s University in Kingston, Ontario have translated the problem of solving a sudoku puzzle into the language of graph theory. The 81 squares in the grid ...