Fractional matching preclusion numbers of Cartesian product graphs

The Cartesian product of two simple graphs G and H is the graph G ❑ H whose vertex set is V (G) x V(H) and whose edge set is the set of all pairs (u1, v1)(u2, v2) such that either u1u2 E E(G) and v1 = v2, or v1v2 E E(H) and u1 = u2. The fractional matching preclusion number of a graph G, denoted by fmp(G), is the minimum number of edges whose deletion results in a graph with no fractional perfect matching. In this paper, we determine fmp(G ❑ H) when H is a cycle or a path of even order; Moreover, given any integers a, b with a > 1 and 0 < b < a + 1, we construct a graph G such that & delta;(G) = a and fmp(G ❑ H) = b when H is a path of odd order.& COPY; 2023 Elsevier B.V. All rights reserved.