Rainbow Tetrahedra in Cayley Graphs

• Autorzy: Italo J. Dejter
• Języki publikacji: EN

Abstrakty

EN

Let Γn be the complete undirected Cayley graph of the odd cyclic group Zn. Connected graphs whose vertices are rainbow tetrahedra in Γn are studied, with any two such vertices adjacent if and only if they share (as tetrahedra) precisely two distinct triangles. This yields graphs G of largest degree 6, asymptotic diameter |V (G)|1/3 and almost all vertices with degree: (a) 6 in G; (b) 4 in exactly six connected subgraphs of the (3, 6, 3, 6)-semi- regular tessellation; and (c) 3 in exactly four connected subgraphs of the {6, 3}-regular hexagonal tessellation. These vertices have as closed neigh- borhoods the union (in a fixed way) of closed neighborhoods in the ten respective resulting tessellations.

Słowa kluczowe

EN

rainbow triangles; rainbow tetrahedra; Cayley graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2015
• Tom: 35
• Numer: 4
• Strony: 733-754

Daty

wydano

2015-11-01

otrzymano

2014-11-06

poprawiono

2015-02-27

zaakceptowano

2015-02-27

online

2015-11-10

Twórcy

autor

Italo J. Dejter

• University of Puerto Rico Rio Piedras, PR 00936-8377

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1834