6 papers
Critical ideals, minimum rank and zero forcing number
Carlos A. Alfaro, Jephian C. -H. Lin
There are profound relations between the zero forcing number and minimum rank of a graph. We study the relation of both parameters with a third one, the algebraic co-rank; that is…
On the error of a priori sampling: zero forcing sets and propagation time
Franklin H. J. Kenter, Jephian C. -H. Lin
Zero forcing is an iterative process on a graph used to bound the maximum nullity. The process begins with select vertices as colored, and the remaining vertices can become colored…
Analogies between the crossing number and the tangle crossing number
Robin Anderson, Shuliang Bai, Fidel Barrera-Cruz +8
Tanglegrams are special graphs that consist of a pair of rooted binary trees with the same number of leaves, and a perfect matching between the two leaf-sets. These objects are of…
The inverse eigenvalue problem of a graph: Multiplicities and minors
Wayne Barrett, Steve Butler, Shaun M. Fallat +5
The inverse eigenvalue problem of a given graph is to determine all possible spectra of real symmetric matrices whose off-diagonal entries are governed by the adjacencies in $G…
Zero forcing number, Grundy domination number, and their variants
Jephian C. -H. Lin
This paper presents strong connections between four variants of the zero forcing number and four variants of the Grundy domination number. These connections bridge the domination p…
Multi-part Nordhaus-Gaddum type problems for tree-width, Colin de Verdière type parameters, and Hadwiger number
Leslie Hogben, Jephian C. -H. Lin, Michael Young
A traditional Nordhaus-Gaddum problem for a graph parameter is to find a (tight) upper or lower bound on the sum or product of and (where denotes…