In 1736, Leonhard Euler showed that there was no way to travel across the Seven Bridges of Königsberg, crossing each bridge a single time and ending up where you started. He did this by showing that ...

Similarly, studies on partial duality in ribbon graphs have provided enumeration techniques and structural results that deepen our understanding of the Euler-genus polynomial, a critical tool in ...

Euler path is one of the most interesting and widely discussed topics in graph theory. An Euler path (or Euler trail) is a path that visits every edge of a graph exactly once. Similarly, an Euler ...

Historically, a Swiss mathematician named Leonhard Euler wrote a journal in 1736 on Graph Theory, titled “Seven Bridge of Konigsberg”. Euler’s analysis discusses the existence of structures that ...

Graph theory is applied in wide area of computer science, including artificial intelligence and operations research. Indeed, graphs are used as models for practical problems. Graph theory, therefore, ...

This paper proposes a new graph-theory-based Euler number computing algorithm. The proposed algorithm only needs to count two bit-quad patterns in the given image, while conventional bit-quad-based ...