Randy Davila

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20242026

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math.CO2024

Comparing the $p$ -independence number of regular graphs to the $q$ -independence number of their line graphs

Yair Caro, Randy Davila, Ryan Pepper

Let $G$ be a simple graph and let $L (G)$ denote the \emph{line graph} of $G$ . A \emph{ $p$ -independent} set in $G$ is a set of vertices $S \subseteq V (G)$ such that the subgraph ind…

math.CO2024

Lower bounds for the total (distance) $k$ -domination number of a graph

Randy Davila

For $k \geq 1$ and a graph $G$ without isolated vertices, a \emph{total (distance) $k$ -dominating set} of $G$ is a set of vertices $S \subseteq V (G)$ such that every vertex in $G$ …

Comparing the p-independence number of regular graphs to the q-independence number of their line graphs

Lower bounds for the total (distance) k-domination number of a graph

Comparing the $p$ -independence number of regular graphs to the $q$ -independence number of their line graphs

Lower bounds for the total (distance) $k$ -domination number of a graph