Title :
Fuzzy Planar Graphs
Author :
Samanta, Sovan ; Pal, Madhumangal
Author_Institution :
Dept. of Math., Joykrishnapur High Sch., Tamluk, India
Abstract :
Fuzzy planar graph is a very important subclass of fuzzy graph. In this paper, two types of edges are mentioned for fuzzy graphs: effective edges and considerable edges. In addition, a comparative study between Kuratowski´s graphs and fuzzy planar graph is made. A new concept of a strong fuzzy planar graph is introduced. Some related results are established. These results have certain applications in subway tunnels, routes, oil/gas pipelines representation, etc. It is also shown that an image can be represented by a fuzzy planar graph, and contraction of such an image can be made with the help of a fuzzy planar graph.
Keywords :
fuzzy set theory; graph theory; image representation; Kuratowski graphs; considerable edges; effective edges; fuzzy planar graphs; image contraction; image representation; Educational institutions; Electronic mail; Graph theory; IP networks; Pipelines; Urban planning; Effective edge; Fuzzy graphs; effective edge; fuzzy graphs; fuzzy planar graphs; image contraction;
Journal_Title :
Fuzzy Systems, IEEE Transactions on
DOI :
10.1109/TFUZZ.2014.2387875
