98 citations · 400 across the 40 of their papers we have counts for
7 papers · 1 filter
Power propagation time and lower bounds for power domination number
Daniela Ferrero, Leslie Hogben, Franklin H. J. Kenter +1
We present a counterexample to a lower bound for the power domination number given in Liao, Power domination with bounded time constraints, J. Comb. Optim. 31 (2016)725-742. We als…
Generalizations of the Strong Arnold Property and the minimum number of distinct eigenvalues of a graph
Wayne Barrett, Shaun Fallat, H. Tracy Hall +3
For a given graph G and an associated class of real symmetric matrices whose off-diagonal entries are governed by the adjacencies in G, the collection of all possible spectra for s…
Power domination and zero forcing
Katherine F. Benson, Daniela Ferrero, Mary Flagg +4
The power domination number arises from the monitoring of electrical networks and its determination is an important problem. Upper bounds for power domination numbers can be obtain…
On the distance spectra of graphs
Ghodratollah Aalipour, Aida Abiad, Zhanar Berikkyzy +8
The distance matrix of a graph is the matrix containing the pairwise distances between vertices. The distance eigenvalues of are the eigenvalues of its distance matrix and…
Fractional Zero Forcing via Three-color Forcing Games
Leslie Hogben, Kevin F. Palmowski, David E. Roberson +1
An -fold analogue of the positive semidefinite zero forcing process that is carried out on the -blowup of a graph is introduced and used to define the fractional positive sem…
Proof of a conjecture of Graham and Lovász concerning unimodality of coefficients of the distance characteristic polynomial of a tree
Ghodratollah Aalipour, Aida Abiad, Zhanar Berikkyzy +4
We establish a conjecture of Graham and Lovász that the (normalized) coefficients of the distance characteristic polynomial of a tree are unimodal; we also prove they are log-conca…