We introduce and study forcing number for fuzzy graphs. Also, we compute zero forcing numbers for some classes of graphs and extend this concept to fuzzy graphs. In this regard we obtain upper bounds for zero forcing of some classes of fuzzy graphs. We will proceed to obtain a new algorithm to computing zero forcing set and finding a formula for zero forcing number, and by some examples we illustrate these notions. Finally, we introduce some applications of fuzzy zero forcing in medical treatments.
AIM Minimum Rank - Special Graphs Work Group (BarioliF., BarrettW., ButlerS., CioabaS., CvetkovicD., FallatS., GodsilC., HaemersW., HogbenL., MikkelsonR., NarayanS., PryporovaO., ScirihaI., SoW., StevanovicD., van der HolstH., MeulenK.V., WeheA.W.), Zero forcing sets and the minimum rank of graphs, Linear Algebra and its Applications428(7) (2008), 1628–1648.
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BarioliF., BarrettW., ButlerS., Cioab̆aS.M., CvetkovícD., FallatS.M., GodsilC., HaemersW., HogbenL., MikkelsonR., NarayanS., PryporovaO., ScirihaI., SoW., StevanovácD., van der HolstH., Vander MeulenK. and WangsnessA., Zero forcing sets and the minimum rank of graphs, Linear Algebra and its Applications428(7) (2008), 1628–1648.
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