$$m$$m-Step fuzzy competition graphs

Presently, fuzzy graph theory has wide applications in engineering and social networks. Based on the applications, different types of fuzzy graphs are defined. Among them the competition graph is significantly used to model ecological problems. This graph is one kind of intersection graph. Different competitions of real world have been designed by fuzzy competition graphs. One generalization of fuzzy competition graph, called $$m$$m-step fuzzy competition graph, is defined in this paper. Some related fuzzy graphs including fuzzy $$m$$m-step neighbourhood graph, fuzzy economic competition graphs and fuzzy $$m$$m-step economic competition graphs are introduced. Some properties of these new graphs have been investigated.

[1]  Madhumangal Pal,et al.  Antipodal Interval-Valued Fuzzy Graphs , 2014, ArXiv.

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

[3]  Madhumangal Pal,et al.  Fuzzy k-competition graphs and p-competition fuzzy graphs , 2013 .

[4]  Madhumangal Pal,et al.  Fuzzy k-competition graphs , 2013, 2013 Science and Information Conference.

[5]  Madhumangal Pal,et al.  Isometry on Interval-valued Fuzzy Graphs , 2014, ArXiv.

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

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

[8]  Jim Hefferon,et al.  Linear Algebra , 2012 .

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

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

[11]  Madhumangal Pal,et al.  Some more results on fuzzy k-competition graphs , 2014 .

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

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

[14]  Madhumangal Pal,et al.  Balanced Interval-Valued Fuzzy Graphs , 2013 .

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

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

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

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

[19]  Bobby Schmidt,et al.  Fuzzy math , 2001 .

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

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

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

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

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

[25]  Muhammad Akram,et al.  Bipolar fuzzy graphs , 2011, Inf. Sci..