A359996 -id:A359996 - cp's OEIS frontend

A359994 Independence number of the 2-Fibonacci digraph of order n.

Original entry on oeis.org

1, 1, 2, 3, 6, 9, 16, 25, 44, 67, 115

Offset: 1

Pontus von Brömssen, Jan 21 2023

See Dalfó and Fiol (2019) or A360000 for the definition of the 2-Fibonacci graph.

a(12) >= 179. - Pontus von Brömssen, Nov 12 2023

C. Dalfó and M. A. Fiol, On d-Fibonacci digraphs, arXiv:1909.06766 [math.CO], 2019.

Cf. A006946, A359995, A359996, A360000.

import networkx as nx
def F(n): return nx.DiGraph(((0,0),(0,1),(1,0))) if n == 1 else nx.line_graph(F(n-1))
def A359994(n): return nx.max_weight_clique(nx.complement(nx.Graph(F(n))),weight=None)[1]

A359995 Number of maximal independent sets in the 2-Fibonacci digraph of order n.

Original entry on oeis.org

2, 3, 4, 10, 32, 184, 5110, 681454

Offset: 1

Pontus von Brömssen, Jan 21 2023

See Dalfó and Fiol (2019) or A360000 for the definition of the 2-Fibonacci graph.

The loop at node 0 is disregarded, so 0 is allowed in the independent sets.

C. Dalfó and M. A. Fiol, On d-Fibonacci digraphs, arXiv:1909.06766 [math.CO], 2019.

Cf. A333077, A359994, A359996, A360000.

import networkx as nx
def F(n): return nx.DiGraph(((0,0),(0,1),(1,0))) if n == 1 else nx.line_graph(F(n-1))
def A359995(n): return sum(1 for c in nx.find_cliques(nx.complement(nx.Graph(F(n)))))

cp's OEIS Frontend

A359994 Independence number of the 2-Fibonacci digraph of order n.

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