OFFSET
1,2
LINKS
Eric Weisstein's World of Mathematics, Fan Graph
Eric Weisstein's World of Mathematics, House Graph
Eric Weisstein's World of Mathematics, Spider Graph
EXAMPLE
For 1 <= n <= 13, the n-node graphs having A352766(n) orientations are listed below. Here, CU(G_1, ..., G_k) denotes the complement of the disjoint union of the graphs G_1, ..., G_k, P_m is the m-node path, and S(m_1, ..., m_k) denotes the spider graph with legs of lengths m_1, ..., m_k.
n = 1: P_1;
n = 2: P_2 and 2*P_1;
n = 3: P_3;
n = 4: CU(P_1, P_1, P_2) (the diamond graph);
n = 5: CU(P_1, P_4) (the fan graph F_{1,4}) and CU(P_1, P_1, P_3) (the house X-graph);
n = 6: CU(P_1, P_2, P_3);
n = 7: CU(P_1, P_2, P_4) and CU(P_1, P_1, P_2, P_3);
n = 8: CU(P_1, S(1, 2, 3));
n = 9: CU(P_1, P_1, S(1, 2, 3)) and CU(P_1, S(1, 2, 4));
n = 10: CU(P_1, P_2, S(1, 2, 3));
n = 11: CU(P_1, P_1, P_2, S(1, 2, 3)) and CU(P_1, P_2, S(1, 2, 4));
n = 12: CU(P_1, P_1, P_2, S(1, 2, 4)) and CU(P_1, P_2, T), where T is any of the three asymmetric trees on 9 nodes (S(1, 2, 5), S(1, 3, 4), or a 7-node path with two additional nodes joined to the 3rd and 4th node of the path, respectively);
n = 13: CU(P_1, P_2, P_3, S(1, 2, 3)), CU(P_1, P_1, P_2, T), where T is any of the three asymmetric trees on 9 nodes, and CU(P_1, P_2, T), where T is any of the six asymmetric trees on 10 nodes.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Pontus von Brömssen, Apr 02 2022
STATUS
approved