\(\DeclarePairedDelimiterX{\Set}[2]{\{}{\}}{#1 \nonscript\;\delimsize\vert\nonscript\; #2}\) \( \DeclarePairedDelimiter{\set}{\{}{\}}\) \( \DeclarePairedDelimiter{\parens}{\left(}{\right)}\) \(\DeclarePairedDelimiterX{\innerproduct}[1]{\langle}{\rangle}{#1}\) \(\newcommand{\ip}[1]{\innerproduct{#1}}\) \(\newcommand{\bmat}[1]{\left[\hspace{2.0pt}\begin{matrix}#1\end{matrix}\hspace{2.0pt}\right]}\) \(\newcommand{\barray}[1]{\left[\hspace{2.0pt}\begin{matrix}#1\end{matrix}\hspace{2.0pt}\right]}\) \(\newcommand{\mat}[1]{\begin{matrix}#1\end{matrix}}\) \(\newcommand{\pmat}[1]{\begin{pmatrix}#1\end{pmatrix}}\) \(\newcommand{\mathword}[1]{\mathop{\textup{#1}}}\)
Needs:
Chordal Graphs ›
Set Partitions ›
Needed by:
Threshold Graphs ›
Links:
Sheet PDF ›
Graph PDF ›

Split Graphs

Why

They are chordal.

Definition

A split graph is an undirected graph whose vertices can be partitioned into two sets such that one set induces a complete subgraph and the other set has no edges between vertices.

Properties

The complement of a split graph is a split graph.

A graph is a split graph if and only if it is chordal and has a chordal complement.1

  1. Future editions will include a proof. ↩︎
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