arXiv subjects
Publications and source records attributed to Stephen Hedetniemi.
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.
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} if the induced subgraph $\langle V \setminus S\rangle$ is either disconnected or a $K_1$. In this paper we introduce the properties split independence and split irredundance. A set $S$ of vertices in a graph $G =(V,E)$ is called a {\em split independent set} if $S$ is independent and the induced subgraph $\langle V \setminus S \rangle$ is either disconnected or a $K_1$. A set $S$ of vertices in a graph $G = (V,E)$ is called a {\em split irredundant set} if for $u \in S$, $u$ has a private neighbor with respect to $V(S)$ and the induced subgraph $\langle V \setminus S\rangle$ is either disconnected or a $K_1$.
An edge dominating set $F$ of a graph $G=(V,E)$ is an \textit{edge cut dominating set} if the subgraph $\langle V,G-F \rangle$ is disconnected. The \textit{edge cut domination number} $γ_{ct}(G)$ of $G$ is the minimum cardinality of an edge cut dominating set of $G.$ In this paper we study the edge cut domination number and investigate its relationships with other parameters of graphs. We also introduce the properties edge cut irredundance and edge cut independence.