3 citations · 4 across the 19 of their papers we have counts for
23 papers
Diamond-free, claw-free cubic graphs are (1, 1, 2, 3)-packing colorable
Sarah E. Anderson, Kirsti Kuenzel, Juan D. Marcano Cuellar
A -packing coloring of a graph is a partition of into two independent sets, a 2-packing, and a -packing. Recently, the question was posed in [A short pr…
Characterizing all nonbipartite well-edge-dominated graphs
Sarah E. Anderson, Kirsti Kuenzel
Given a graph , a set of edges is an edge dominating set of if every edge in is either in or adjacent to an edge in . A graph is said to be well-edge-domi…
Characterizing all -free well-edge-dominated graphs of girth 3
Sarah E. Anderson, Kirsti Kuenzel
Given a graph , a set of edges is an edge dominating set if all edges in are either in or adjacent to an edge in . is said to be well-edge-dominated if every…
Isolation number: Cartesian and lexicographic products and generalized Sierpiński graphs
Bostjan Bresar, Tanja Dravec, Daniel P. Johnston +3
The isolation number of a graph is the minimum cardinality of a set such that the subgraph induced by the vertices that are not in the union of the close…
Well-hued graphs with first difference two
Geoffrey Boyer, Kirsti Kuenzel, Jeremy Lyle +1
A graph is said to be well-hued if every maximal -colorable subgraph of has the same order . Therefore, if is well-hued, we can associate with a sequence $\…
Well-edge-dominated graphs containing triangles
Jake Berg, Perryn Chang, Claire Kaneshiro +4
A set of edges in a graph is an edge dominating set if every edge in is either in or shares a vertex with an edge in . is said to be well-edge-dominated if a…
Claw-free cubic graphs are -colorable
Boštjan Brešar, Kirsti Kuenzel, Douglas F. Rall
A -coloring of a graph is a partition of its vertex set into four sets two of which are independent and the other two are -packings. In this paper, we prove that ever…
Isolation game on graphs
Boštjan Brešar, Tanja Dravec, Daniel P. Johnston +2
Given a graph and a family of graphs , an -isolating set, as introduced by Caro and Hansberg, is any set such that contains no member…
Orientable total domination in graphs
Sarah E. Anderson, Tanja Dravec, Daniel Johnston +1
Given a directed graph , a set is a total dominating set of if each vertex in has an in-neighbor in . The total domination number of , denoted $…
The number of independent sets in bipartite graphs and benzenoids
Michael Han, Sycamore Herlihy, Kirsti Kuenzel +2
Given a graph , we study the number of independent sets in , denoted . This parameter is known as both the Merrifield-Simmons index of a graph as well as the Fibonacci…
A characterization of well-dominated Cartesian products
Kirsti Kuenzel, Douglas F. Rall
A graph is well-dominated if all its minimal dominating sets have the same cardinality. In this paper we prove that at least one factor of every connected, well-dominated Cartesian…
Graphs with equal Grundy domination and independence number
Gábor Bacsó, Boštjan Brešar, Kirsti Kuenzel +1
The Grundy domination number, , of a graph is the maximum length of a sequence of vertices in such that for every $i\in \{2,\ldots,…
Loop zero forcing and grundy domination in planar graphs and claw-free cubic graphs
Alex Domat, Kirsti Kuenzel
Given a simple, finite graph with vertex set , we define a zero forcing set of as follows. Choose and color all vertices of blue and all vertices in…
Orientable domination in product-like graphs
Sarah Anderson, Boštjan Brešar, Sandi Klavžar +2
The orientable domination number, , of a graph is the largest domination number over all orientations of . In this paper, is studied on different p…
Power domination in cubic graphs and Cartesian products
Sarah E. Anderson, Kirsti Kuenzel
The power domination problem focuses on finding the optimal placement of phase measurement units (PMUs) to monitor an electrical power network. In the context of graphs, the power…
Graphs which satisfy a Vizing-like bound for power domination of Cartesian products
Sarah E. Anderson, Kirsti Kuenzel, Houston Schuerger
Power domination is a two-step observation process that is used to monitor power networks and can be viewed as a combination of domination and zero forcing. Given a graph , a su…
On independent domination in direct products
Kirsti Kuenzel, Douglas F. Rall
In \cite{nr-1996} Nowakowski and Rall listed a series of conjectures involving several different graph products. In particular, they conjectured that wh…
On well-edge-dominated graphs
Sarah E. Anderson, Kirsti Kuenzel, Douglas F. Rall
A graph is said to be well-edge-dominated if all its minimal edge dominating sets are minimum. It is known that every well-edge-dominated graph is also equimatchable, meaning t…
Domination in digraphs and their products
Boštjan Brešar, Kirsti Kuenzel, Douglas F. Rall
A dominating (respectively, total dominating) set of a digraph is a set of vertices in such that the union of the closed (respectively, open) out-neighborhoods of verti…
On well-dominated graphs
Sarah E. Anderson, Kirsti Kuenzel, Douglas F. Rall
A graph is \emph{well-dominated} if all of its minimal dominating sets have the same cardinality. We prove that at least one of the factors is well-dominated if the Cartesian produ…
Graphs in which all maximal bipartite subgraphs have the same order
Wayne Goddard, Kirsti Kuenzel, Eileen Melville
Motivated by the concept of well-covered graphs, we define a graph to be well-bicovered if every vertex-maximal bipartite subgraph has the same order (which we call the bipartite n…
Graphs with a unique maximum open packing
Boštjan Brešar, Kirsti Kuenzel, Douglas F. Rall
A set of vertices in a graph is an open packing if (open) neighborhoods of any two distinct vertices in are disjoint. In this paper, we consider the graphs that have a uniq…
On well-covered direct products
Kirsti Kuenzel, Douglas F. Rall
A graph is well-covered if all maximal independent sets of have the same cardinality. In 1992 Topp and Volkmann investigated the structure of well-covered graphs that have…