R. Laskar

activity

20152019

collaborators

6 papers

math.CO2019

Properties of Partial Dominating Sets of Graphs

Benjamin M. Case, Todd Fenstermacher, Soumendra Ganguly +1

A set $S \subseteq V$ is a dominating set of $G$ if every vertex in $V - S$ is adjacent to at least one vertex in $S$ . The domination number $γ (G)$ of $G$ equals the minimum cardina…

math.CO2019

$β$ -Packing Sets in Graphs

Benjamin M. Case, Evan M. Haithcock, Renu C. Laskar

A set $S \subseteq V$ is $α$ -dominating if for all $v \in V - S$ , $∣ N (v) \cap S ∣ \geq α ∣ N (v) ∣.$ The $α$ -domination number of $G$ equals the minimum cardinality of an $α$ -dominating se…

math.CO2017

Partial Domination in Graphs

Benjamin M. Case, Stephen T. Hedetniemi, Renu C. Laskar +1

A set $S \subseteq V$ is a dominating set of $G$ if every vertex in $V - S$ is adjacent to at least one vertex in $S$ . The domination number $γ (G)$ of $G$ equals the minimum cardina…

math.CO2016

Split Domination, Independence, and Irredundance in Graphs

Stephen Hedetniemi, Fiona Knoll, Renu Laskar

In 1978, Kulli and Janakiram \citep{KulliJanakiramSplit} defined the split dominating set: a dominating set $S$ of vertices in a graph $G = (V, E)$ is called {\em split dominating}…

math.CO2016

Edge Cut Domination, Irredundance, and Independence in Graphs

Todd Fenstermacher, Stephen Hedetniemi, Renu Laskar

An edge dominating set $F$ of a graph $G = (V, E)$ is an \textit{edge cut dominating set} if the subgraph $⟨ V, G - F ⟩$ is disconnected. The \textit{edge cut domination numb…

math.CO2015

Cycle Domination, Independence and Irredundance in graphs

Amy Grady, Fiona Knoll, Renu Laskar +1

A set $S$ of vertices in a graph $G = (V, E)$ is called {\em cycle independent} if the induced subgraph $⟨ S ⟩$ is acyclic, and called {\em odd-cycle indepdendet} if $\l…