Minimum rank, maximum nullity and zero forcing number for selected graph families

The minimum rank of a simple graph G is dened to be the smallest possible rank over all symmetric real matrices whose ijth entry (for i 6 j) is nonzero whenever fi;jg is an edge in G and is zero otherwise. Maximum nullity is taken over the same set of matrices, and the sum of maximum nullity and minimum rank is the order of the graph. The zero forcing number is the minimum size of a zero forcing set of vertices and bounds the maximum nullity from above. This paper denes the graph families ciclos and estrellas and establishes the minimum rank and zero forcing number of several of these families. In particular, these families provide the examples showing that the maximum nullity of a graph and its dual may dier, and similarly for zero forcing number.