We show that the groupoids of two directed graphs are isomorphic if and only if the two graphs are orbit equivalent by an orbit equivalence that preserves isolated eventually periodic points. We also ...

Additionally, research on planar graphs has yielded new insights into the anti-Ramsey numbers for paths and cycles, thereby bridging classical graph theory with geometric constraints [3].

Commuting Graphs and Finite Group Theory Publication Trend The graph below shows the total number of publications each year in Commuting Graphs and Finite Group Theory.

These mathematical phenomena appear in everything from entanglement interactions in quantum mechanics to the trajectory of a disease spreading through a population. If a pharmacologist wanted to model ...

The study of such graphs is called graph theory. Engineers need to find planarity in a graph when, for example, they are designing a computer chip without a crossed wire.