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Iterated neighborhood graphs

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Sonntag M., Teichert H.-M.

Discussiones Mathematicae Graph Theory

2012

tom 32

nr 3

403-417

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.

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1 Discussiones Mathematicae Graph Theory

1 Sonntag M.

1 Teichert H.-M.

1 2012

Wyniki wyszukiwania

Iterated neighborhood graphs