Introduction One of the most seminal and revolutionary ideas of the 19th century was that of a group, which forms the basis for all subsequent developments in mathematics and science, and is a corn...

Imagine standing on an archipelago, its islands connected by bridges, and facing a seemingly simple question: can you start at one point, cross each bridge exactly once, and return to where you beg...

Introduction It is undoubtedly a difficult concept to grasp—one of the most abstract that undergraduate students might encounter during their studies. Yet, it is so ubiquitous that nearly every sci...

Introduction Graphs are widely used to model real-world systems such as social networks, communication channels, and dependency structures. In directed graphs, cycles are particularly significant, ...