Classification of α-Ricci flat graphs with girth at least five

Abstract Lin, Lu and Yau classified Ricci flat graphs with girth at least 5 in Lin et al., 2014 [7] and Cushing et al., 2018 [4,5]. In Lin et al., 2014, they defined α -Ricci curvature for the definition of Ricci curvature. We will classify α -Ricci flat graphs with girth at least 5 for all α ∈ ( 0 , 1 ) .