Fuzzy Tolerance Graph

In this paper, we dene fuzzy tolerance, fuzzy tolerance graph, fuzzy bounded tol-erance graph, fuzzy interval containment graph and regular representation of fuzzytolerance graph, fuzzy unit tolerance graph and proper tolerance graph. Also somebasic theorems related to the stated graphs have been presented.

[1]  Madhumangal Pal,et al.  Intersection Graphs: An Introduction , 2014, ArXiv.

[2]  Fred S. Roberts,et al.  Applications of edge coverings by cliques , 1985, Discret. Appl. Math..

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

[4]  Shmuel Zaks,et al.  The Recognition of Tolerance and Bounded Tolerance Graphs , 2011, SIAM J. Comput..

[5]  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).

[6]  James F. Allen.  Maintaining knowledge about temporal intervals , 1983, CACM.

[7]  Laurent Krähenbühl,et al.  Tolerance synthesis using bond graph inversion and fuzzy logic , 2013, 2013 IEEE International Conference on Mechatronics (ICM).

[8]  Terry A. McKee,et al.  p-Competition Numbers , 1993, Discret. Appl. Math..

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

[10]  M. McAllister,et al.  Fuzzy intersection graphs , 1988 .

[11]  Characterizations of fuzzy interval graphs , 1994 .

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

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

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

[15]  Stefan Felsner.  Tolerance Graphs and Orders , 1992, WG.

[16]  Peter C. Fishburn,et al.  Proper and Unit Tolerance Graphs , 1995, Discret. Appl. Math..