Iterated neighborhood graphs

• Autorzy: Martin Sonntag , Hanns-Martin Teichert
• Języki publikacji: EN

Abstrakty

EN

The neighborhood graph N(G) of a simple undirected graph G = (V,E) is the graph $(V,E_N)$ where $E_N$ = {{a,b} | a ≠ b, {x,a} ∈ E and {x,b} ∈ E for some x ∈ V}. It is well-known that the neighborhood graph N(G) is connected if and only if the graph G is connected and non-bipartite.
We present some results concerning the k-iterated neighborhood graph $N^k(G) : = N(N(...N(G)))$ of G. In particular we investigate conditions for G and k such that $N^k(G)$ becomes a complete graph.

Słowa kluczowe

EN

neighborhood graph; 2-step graph; neighborhood completeness number

Kategorie tematyczne

• 05C12: Distance in graphs
• 05C76: Graph operations (line graphs, products, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2012
• Tom: 32
• Numer: 3
• Strony: 403-417

Daty

wydano

2012

otrzymano

2011-01-12

poprawiono

2011-07-14

zaakceptowano

2011-07-18

Twórcy

autor

Martin Sonntag

• Faculty of Mathematics and Computer Science, Technische Universität Bergakademie Freiberg, D-09599 Freiberg, Germany

autor

Hanns-Martin Teichert

• Institute of Mathematics, University of Lübeck, D-23560 Lübeck, Germany

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1610