Clayton State University

output

20082024

most citedRevisiting with Chandra the Scaling Relations of the X-ray Emission Components (Binaries, Nuclei and Hot Gas) of Early Type Galaxies

212 citations

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12 papers · 1 filter

math.CO2021★ 3 cited

Grundy domination of forests and the strong product conjecture

Kayla Bell, Keith Driscoll, Elliot Krop +1

A maximum sequence $S$ of vertices in a graph $G$ , so that every vertex in $S$ has a neighbor which is independent, or is itself independent, from all previous vertices in $S$ , is…

math.CO2019★ 4 cited

Upper bounds for inverse domination in graphs

Elliot Krop, Jessica McDonald, Gregory J. Puleo

In any graph $G$ , the domination number $γ (G)$ is at most the independence number $α (G)$ . The Inverse Domination Conjecture says that, in any isolate-free $G$ , there exists pair of…

math.CO2018★ 5 cited

Ramsey and Gallai-Ramsey numbers for two classes of unicyclic graphs

Zhao Wang, Yaping Mao, Colton Magnant +1

Given a graph $G$ and a positive integer $k$ , define the \emph{Gallai-Ramsey number} to be the minimum number of vertices $n$ such that any $k$ -edge coloring of $K_{n}$ contains eith…

math.CO2018★ 15 cited

A Vizing-type result for semi-total domination

John Asplund, Randy Davila, Elliot Krop

A set of vertices $S$ in a simple isolate-free graph $G$ is a semi-total dominating set of $G$ if it is a dominating set of $G$ and every vertex of $S$ is within distance 2 or less…

math.CO2017★ 2 cited

On a Vizing-type integer domination conjecture

Randy Davila, Elliot Krop

Given a simple graph $G$ , a dominating set in $G$ is a set of vertices $S$ such that every vertex not in $S$ has a neighbor in $S$ . Denote the domination number, which is the size…

math.CO2016★ 3 cited

Vizing's conjecture: a two-thirds bound for claw-free graphs

Elliot Krop

We show that for any claw-free graph $G$ and any graph $H$ , $γ (G □ H) \geq \frac{2}{3} γ (G) γ (H)$ , where $γ (G)$ is the domination number of $G$ .