Families of graphs with maximum nullity equal to zero forcing number
نویسندگان
چکیده
منابع مشابه
Ela 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 کاملMinimum Rank, Maximum Nullity, and Zero Forcing of Graphs
Combinatorial matrix theory, which involves connections between linear algebra, graph theory, and combinatorics, is a vital area and dynamic area of research, with applications to fields such as biology, chemistry, economics, and computer engineering. One area generating considerable interest recently is the study of the minimum rank of matrices associated with graphs. Let F be any field. For a...
متن کاملEla 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 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Special Matrices
سال: 2018
ISSN: 2300-7451
DOI: 10.1515/spma-2018-0006