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 ...

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 ...

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 ...

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 ...

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 ...

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 ...