MINIMUM ZERO-FORCING SETS OF VARIOUS GRAPHS: INSIGHTS AND REAL-WORLD APPLICATIONS

Abstract [English]

Let each vertex of a graph G = (V (G), E(G)) be given one of two colours, say, “black” and “white”. Let Z denote the (initial) set of black vertices of G. The colour-change rule converts the colour of a vertex from white to black if the white vertex is the only white neighbour of a black vertex. Set Z is a zero forcing set of G if all vertices of G are turned black after finitely many applications of the colour-change rule. The zero forcing number of G is the minimum of |Z| overall zero forcing sets Z ⊂ V (G). This article explores the zero forcing in some graphs G. Additionally, it delves into the precise determination of minimum zero forcing set for certain well-known graphs.