University of Isfahan Transactions on Combinatorics 2251-8657 9 4 2020 12 01 Zero-sum flow number of categorical and strong product of graphs 181 199 24517 10.22108/toc.2020.120375.1689 EN Muhammad Aamer Rashid Department of Mathematics, COMSATS University Islamabad, Lahore Campus, 54000, Pakistan Sarfraz Ahmad Department of Mathematics, COMSATS University Islamabad, Lahore Campus, 54000, Pakistan Muhammad Farhan Hanif Department of Mathematics, COMSATS University Islamabad, Lahore Campus, 54000, Pakistan Muhammad Kamran Siddiqui Department of Mathematics COMSATS University Islamabad, Lahore Campus, 54000, Pakistan Muhammad Naeem Department of Mathematics, The University of Okara, Pakistan Journal Article 2019 12 07 A zero-sum flow is an assignment of nonzero integers to the edges such that the sum of the values of all edges incident with each vertex is zero, and we call it a zero-sum $k$-flow if the absolute values of edges are less than $k$. We define the zero-sum flow number of $G$ as the least integer $k$ for which $G$ admitting a zero sum $k$-flow.?<br />In this paper we gave complete zero-sum flow and zero sum numbers for categorical and strong product of two graphs namely cycle and paths. https://toc.ui.ac.ir/article_24517_97a6195eb2729b9bbe843c44360c7b64.pdf