Graph theory includes two unavoidable graphs, namely Euler graphs and Hamiltonian graphs. In this study, generalized fuzzy Euler graphs (GFEGs) and generalized fuzzy Hamiltonian graphs (GFHGs) are defined to express uncertain system like routes, networks. Here, even degrees of all vertices of graphs do not assure that the graphs are GFEG. Similarly, other properties of crisp Euler graphs and crisp Hamiltonian graphs are tested. Two algorithms are prepared to find Eulerian circuit in GFEGs and Hamiltonian circuit in GFHGs. In modern life, planning of efficient routes is very important for business and industry purposes. An application on planning of routes is described.
Bibliographical noteFunding Information:
This work was supported by the research fund of Hanyang University (HY-2018-F), (Project Number 201800000001370).
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Artificial Intelligence