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We study nonexistence and existence of nontrivial positive solutions to thefollowing semilinear elliptic inequality involving gradient terms  \[  \Delta u+u^p\left|\nabla u\right|^q\leq0,  \] on weighted graphs, where $(p,q)\in\mathbb{R}^2$. We give a completeclassification of $(p,q)$ under which sharp volume growth assumptions areestablished.

Sharp Liouville type results for semilinear elliptic inequalities involving gradient terms on weighted graphs