Some more results on fuzzy k-competition graphs

Fuzzy competition graph as the generalization of competition graph is introduced here. Fuzzy k-competition graph as a special type of fuzzy competition graph is defined here along with fuzzy isolated vertices. The fuzzy competition number is also introduced and investigated several properties. Isomorphism properties on fuzzy competition graphs are discussed.

[1]  Partha Ghosh,et al.  Fuzzy graph representation of a fuzzy concept lattice , 2010, Fuzzy Sets Syst..

[2]  Madhumangal Pal.  Fuzzy Tolerance Graph , 2012 .

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

[4]  Madhumangal Pal,et al.  Irregular Bipolar Fuzzy Graphs , 2012, ArXiv.

[5]  Han Hyuk Cho,et al.  The m-step competition graph of a digraph , 2000, Discret. Appl. Math..

[6]  Suh-Ryung Kim.  Graphs with one hole and competition number one , 2005 .

[7]  Azriel Rosenfeld,et al.  Strong arcs in fuzzy graphs , 2003, Inf. Sci..

[8]  Azriel Rosenfeld,et al.  ON DEGREES OF END NODES AND CUT NODES IN FUZZY GRAPHS , 2004 .

[9]  S. Somasundaram,et al.  Domination in fuzzy graphs - I , 1998, Pattern Recognit. Lett..

[10]  V. Novák.  Fuzzy sets and their applications , 1989 .

[11]  S. K. Ayyaswamy,et al.  On Strong(Weak) Domination in Fuzzy Graphs , 2010 .

[12]  Debra D. Scott.  The competition-common enemy graph of a digraph , 1987, Discret. Appl. Math..

[13]  Yoshio Sano.  The competition-common enemy graphs of digraphs satisfying Conditions C(p) and C 0 (p) , 2010 .

[14]  P.S. Nair.  Perfect and precisely perfect fuzzy graphs , 2008, NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society.

[15]  Javier Yáñez,et al.  Coloring fuzzy graphs , 2005 .

[16]  S.-C. Cheng,et al.  Cliques and fuzzy cliques in fuzzy graphs , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

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

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

[19]  Muhammad Akram,et al.  Bipolar fuzzy graphs with applications , 2013, Knowl. Based Syst..

[20]  Suzanne M. Seager,et al.  Niche graphs , 1989, Discret. Appl. Math..

[21]  Muhammad Akram,et al.  Interval-valued fuzzy graphs , 2012, Comput. Math. Appl..

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

[23]  Madhumangal Pal,et al.  Fuzzy Threshold Graphs , 2011 .

[24]  Terry A. McKee,et al.  2-Competition Graphs , 1992, SIAM J. Discret. Math..

[25]  Sunil Mathew,et al.  Node connectivity and arc connectivity of a fuzzy graph , 2010, Inf. Sci..

[26]  L. Kóczy.  Fuzzy graphs in the evaluation and optimization of networks , 1992 .

[27]  Madhumangal Pal,et al.  Bipolar Fuzzy Hypergraphs , 2012 .

[28]  Clyde L. Monma,et al.  Tolerance graphs , 1984, Discret. Appl. Math..

[29]  Yoshio Sano.  Characterizations of competition multigraphs , 2009, Discret. Appl. Math..

[30]  Kiran R. Bhutani,et al.  On M-strong fuzzy graphs , 2003, Inf. Sci..

[31]  A. Nagoor Gani,et al.  Insensitive Arc in Domination of Fuzzy Graph , 2011 .

[32]  K. Radha.  On Regular Fuzzy Graphs , 2008 .

[33]  John N. Mordeson,et al.  Successor and Source of (Fuzzy) Finite State Machines and (Fuzzy) Directed Graphs , 1996, Inf. Sci..

[34]  Terry A. McKee,et al.  p-competition graphs , 1995 .

[35]  Martin Sonntag,et al.  Competition hypergraphs , 2004, Discret. Appl. Math..

[36]  Robert C. Brigham,et al.  Tolerance competition graphs , 1995 .