Zero forcing number, path cover number, and maximum nullity of cacti
نویسندگان
چکیده
منابع مشابه
Ela Positive Semidefinite Maximum Nullity and Zero Forcing Number
The zero forcing number Z(G) is used to study the minimum rank/maximum nullity of the family of symmetric matrices described by a simple, undirected graph G. The positive semidefinite zero forcing number is a variant of the (standard) zero forcing number, which uses the same definition except with a different color-change rule. The positive semidefinite maximum nullity and zero forcing number f...
متن کاملPositive semidefinite maximum nullity and zero forcing number
The zero forcing number Z(G) is used to study the minimum rank/maximum nullity of the family of symmetric matrices described by a simple, undirected graph G. The positive semidefinite zero forcing number is a variant of the (standard) zero forcing number, which uses the same definition except with a different color-change rule. The positive semidefinite maximum nullity and zero forcing number f...
متن کاملEla the Maximum Nullity of a Complete Subdivision Graph Is Equal to Its Zero Forcing Number∗
Barrett et al. asked in [W. Barrett et al. Minimum rank of edge subdivisions of graphs. Electronic Journal of Linear Algebra, 18:530–563, 2009.], whether the maximum nullity is equal to the zero forcing number for all complete subdivision graphs. We prove that this equality holds. Furthermore, we compute the value of M(F, G̊) = Z(G̊) by introducing the bridge tree of a connected graph. Since this...
متن کاملEla Minimum Rank, Maximum Nullity, and Zero Forcing Number of Simple Digraphs
A simple digraph describes the off-diagonal zero-nonzero pattern of a family of (not necessarily symmetric) matrices. Minimum rank of a simple digraph is the minimum rank of this family of matrices; maximum nullity is defined analogously. The simple digraph zero forcing number is an upper bound for maximum nullity. Cut-vertex reduction formulas for minimum rank and zero forcing number for simpl...
متن کاملOn the zero forcing number of some Cayley graphs
Let Γa be a graph whose each vertex is colored either white or black. If u is a black vertex of Γ such that exactly one neighbor v of u is white, then u changes the color of v to black. A zero forcing set for a Γ graph is a subset of vertices Zsubseteq V(Γ) such that if initially the vertices in Z are colored black and the remaining vertices are colored white, then Z changes the col...
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ژورنال
عنوان ژورنال: Involve, a Journal of Mathematics
سال: 2011
ISSN: 1944-4184,1944-4176
DOI: 10.2140/involve.2011.4.277