Tolerance graphs were introduced in 1982 by M. C. Golumbic and C. L. Monma as a generalization of interval graphs. In this paper, we introduce tolerance fuzzy graphs as a generalization of tolerance graphs, and apply them to a modeling of a transmission of airborne diseases.
GolumbicM.C. and MonmaC.L., A generalization of interval graphs with tolerances, Proceedings of the thirteenth Southeastern conference on combinatorics, graph theory and computing (Boca Raton, Fla, Congr Numer35 (1982), 321–331.
GrötschelM., LovászL. and SchrijverA., Polynomial algorithms for perfect graphs, Ann Discr Math21 (1984), 325–356.
15.
JungnickelD., Graphs, Networks and Algorithms, 2nd edition, Springer Berlin Heidelberg New York, 2005.
16.
KarpR.M., Reducibility among combinatorial problems. In: R.E. Miller, J.W. Thatcher (eds), Complexity of Computer Computations, Plenum Press, New York, 1972, pp. 85–103.
17.
LovászL., A characterization of perfect graphs, J Combin Theory B13 (1972), 95–98.
18.
McAllisterL.M.N., Fuzzy intersection graphs, Intl J Computers in Mathematies with Applications5 (1988), 871–886.
19.
NiskanenS. and ÖstergardP.R.J., Cliquer user’s guide, version 1.0, Communications Laboratory, Helsinki University of Technology, Espoo, Finland, Tech.Rep. T48, 2003.
20.
PostavaruO., AntonS.R. and TomaA., COVID-19 pandemic and chaos theory, Math Comput Simulation181 (2021), 138–149.
21.
RosenfeldA., Fuzzy graphs, in: L.A. Zadeh, K.S. Fu, M. Shimura (Eds.), Fuzzy Sets and Their Applications, Academic press, 1975, pp. 77–95.
SahooS. and PalM., Intuitionistic fuzzy tolerance graphs with application, J Appl Math Comput55 (2017), 495–511.
24.
SamantaS. and PalM., Fuzzy tolerance graphs, Int J Latest Trend Math1 (2011), 57–67.
25.
ZadehL.A., Fuzzy sets, Information and Control8 (1965), 338–353.
26.
ZhuH., LiY., JinX., HuangJ., LiuX., QianY. and TanJ., Transmission dynamics and control methodology of COVID-19: A modeling study, Appl Math Model89 (2021), 1983–1998.
