On the line graphs of the complete \(r\)-partite graphs (Q1363708)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the line graphs of the complete \(r\)-partite graphs |
scientific article; zbMATH DE number 1047095
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the line graphs of the complete \(r\)-partite graphs |
scientific article; zbMATH DE number 1047095 |
Statements
On the line graphs of the complete \(r\)-partite graphs (English)
0 references
5 January 1998
0 references
Let \(G\) be a graph with \(n\) vertices and \(\{V_1,\dots,V_r\}\) a partition of \(V(G)\) with \(|V_i|= p_i\) \((1\leq i\leq r)\) where \(p_1\leq\cdots\leq p_r\). Here the author proves that the vertex-connectivity of the line graph of the complete \(r\)-partite graph \(G\) equals \(2n-2-p_{r-1}- p_r\), which is the minimum degree.
0 references
vertex-connectivity
0 references
line graph
0 references
complete \(r\)-partite graph
0 references
