Publikacije Elektrotehnickog fakulteta - serija: matematika 2003 Issue 14, Pages: 1-3
doi:10.2298/PETF0314001M
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Antiregular graphs are universal for trees

Merris Russell

A graph on n vertices is antiregular if its vertex degrees take on n − 1 different values. For every n ≥ 2 there is a unique connected antiregular graph on n vertices. Call it An. (The unique disconnected antiregular graph on n vertices is Acn.) The main result of this note is that every tree on n vertices is isomorphic to a subgraph of An.

Keywords: Adjacency matrix, chordal graph, chromatic number, Laplacian matrix, matching number, perfect graph, threshold graph

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