On Vertex Types of Graphs

On Vertex Types of Graphs

The vertices of a graph are classified into seven types by J.T. Hedetniemi, S.M. Hedetniemi, S.T. Hedetniemi and T.M. Lewis and they ask the following questions: (1) What is the smallest order n of a graph having n - 2 very typical vertices or n - 2 typical vertices? (2) What is the smallest order o...

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Veröffentlicht in:Graphs and combinatorics 2018-09, Vol.34 (5), p.889-900
Hauptverfasser: Qiao, Pu, Zhan, Xingzhi
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Engineering Design
Graph theory
Graphs
Mathematics
Mathematics and Statistics
Original Paper
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Zusammenfassung:The vertices of a graph are classified into seven types by J.T. Hedetniemi, S.M. Hedetniemi, S.T. Hedetniemi and T.M. Lewis and they ask the following questions: (1) What is the smallest order n of a graph having n - 2 very typical vertices or n - 2 typical vertices? (2) What is the smallest order of a pantypical graph? We answer these two questions and determine all the possible orders of the graphs in these three classes in this paper.
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-018-1919-3