S. Hedetniemi

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20162025

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5 papers · 1 filter

math.CO2025

On maximizing private neighbors in graphs

Stephen T. Hedetniemi, Douglas F. Rall

Given a set $U \subset V$ of vertices in a graph $G = (V, E)$ , a {\it private neighbor with respect to the set $U$ } is any vertex $w \in V$ having precisely one neighbor, say $v$ ,…

math.CO2018

$P$ -Matchings in Graphs: A Brief Survey with Some Open Problems

Todd Fenstermacher, Soumendra Ganguly, Stephen Hedetniemi +1

For a graph $G = (V, E),$ a matching $M$ is a set of independent edges. The topic of matchings is well studied in graph theory. In this paper many varieties of matchings are discussed…

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…