3-Trees with Diameter 2

A -tree is a graph that can be formed by starting with and iterating the operation of making a new vertex adjacent to all the vertices of a -clique of the existing graph. A structural characterization of 3-trees with diameter at most 2 is proven. This implies a corollary for planar 3-trees which leads to a description of their degree sequences.

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Publication Details

Journal
Ars Combinatoria
Published
2024-12-31
DOI
https://doi.org/10.61091/ars161-10
Primary Topic
Advanced Graph Theory Research
Type
article
Field-Weighted Citation Impact
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3-Trees with Diameter 2

Allan Bickle
Ars Combinatoria
Advanced Graph Theory Research
article

3-Trees with Diameter 2

Allan Bickle
article en

Abstract

A -tree is a graph that can be formed by starting with and iterating the operation of making a new vertex adjacent to all the vertices of a -clique of the existing graph. A structural characterization of 3-trees with diameter at most 2 is proven. This implies a corollary for planar 3-trees which leads to a description of their degree sequences.

Ars CombinatoriaVol. 161(1)
Purdue University West Lafayette (US)
Life in Land
Openalex Percentile: Top 70%
Advanced Graph Theory Research
DOIOpen Access PDFOpenAlex
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3-Trees with Diameter 2 — Allan Bickle · Ars Combinatoria (2024) | TGRS Research Map | TGRS