Intuitionistic Fuzzy Planar Graphs

Graph theory has numerous applications in modern sciences and technology. Atanassov introduced the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. Intuitionistic fuzzy set has shown advantages in handling vagueness and uncertainty compared to fuzzy set. In this paper, we apply the concept of intuitionistic fuzzy sets to multigraphs, planar graphs, and dual graphs. We introduce the notions of intuitionistic fuzzy multigraphs, intuitionistic fuzzy planar graphs, and intuitionistic fuzzy dual graphs and investigate some of their interesting properties. We also study isomorphism between intuitionistic fuzzy planar graphs.

[1]  Madhumangal Pal,et al.  New concepts of fuzzy planar graphs , 2014 .

[2]  Khidir M. Ali,et al.  Applications of Graph Theory in Computer Science , 2011, 2011 Third International Conference on Computational Intelligence, Communication Systems and Networks.

[3]  John N. Mordeson,et al.  Operations on Fuzzy Graphs , 1994, Inf. Sci..

[4]  R. Yager.  ON THE THEORY OF BAGS , 1986 .

[5]  Changiz Eslahchi,et al.  Vertex-strength of fuzzy graphs , 2006, Int. J. Math. Math. Sci..

[6]  Muhammad Akram,et al.  Intuitionistic Fuzzy Cycles and Intuitionistic Fuzzy Trees , 2014, TheScientificWorldJournal.

[7]  Prabir Bhattacharya,et al.  Some remarks on fuzzy graphs , 1987, Pattern Recognit. Lett..

[8]  Tina Anggitta Novia,et al.  Complement of a Fuzzy Graph , 2009 .

[9]  Krassimir T. Atanassov,et al.  Operations on intuitionistic fuzzy graphs , 2009, 2009 IEEE International Conference on Fuzzy Systems.

[10]  Lotfi A. Zadeh,et al.  Similarity relations and fuzzy orderings , 1971, Inf. Sci..

[11]  Krassimir T. Atanassov,et al.  Intuitionistic Fuzzy Sets - Theory and Applications , 1999, Studies in Fuzziness and Soft Computing.

[12]  Ronald R. Yager,et al.  Intuitionistic fuzzy graph interpretations of multi-person multi-criteria decision making , 2003, EUSFLAT Conf..

[13]  Madhumangal Pal,et al.  Concept of fuzzy planar graphs , 2013, 2013 Science and Information Conference.

[14]  Eman H. Ouda,et al.  FUZZY DUAL GRAPH , 2009 .

[15]  R. Parvathi,et al.  Intuitionistic Fuzzy Graphs , 2006 .

[16]  Muhammad Akram,et al.  Certain Types of Interval-Valued Fuzzy Graphs , 2013, J. Appl. Math..

[17]  Muhammad Akram,et al.  $$m$$m-Step fuzzy competition graphs , 2015 .

[18]  Sunil Jacob John,et al.  Intuitionistic Fuzzy Multisets And Its Application in Medical Diagnosis , 2012 .

[19]  John N. Mordeson,et al.  Fuzzy Graphs and Fuzzy Hypergraphs , 2000, Studies in Fuzziness and Soft Computing.

[20]  B. Davvaz,et al.  Strong Intuitionistic Fuzzy Graphs , 2012 .

[21]  Sunil Mathew,et al.  Types of arcs in a fuzzy graph , 2009, Inf. Sci..

[22]  Wieslaw A. Dudek,et al.  Intuitionistic fuzzy hypergraphs with applications , 2013, Inf. Sci..