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A178435 Number of acyclic orientations of the Triangle Graph of order n. 11
1, 6, 162, 19602, 10619910, 25753129470, 279488630719746, 13573527285845525634, 2949851294016821586137934, 2868652614504623418332698354038, 12483073717920041560887416137620435882, 243068197882943244196175524589364487906969746, 21178547618859581967063811182618272071362317831449326 (list; graph; refs; listen; history; text; internal format)



The Triangle Graph of order n has n rows with i vertices in row i. Each vertex is connected to the neighbors in the same row and up to two vertices in each of the neighboring rows. The Graph has A000217(n) vertices and 3*A000217(n-1) edges altogether.

An acyclic orientation is an assignment of a direction to each edge such that no cycle in the graph is consistently oriented. Stanley showed that the number of acyclic orientations of a graph G is equal to the absolute value of the chromatic polynomial X_G(q) evaluated at q=-1.


Table of n, a(n) for n=1..13.

Richard P. Stanley, Acyclic Orientations of Graphs, Discrete Mathematics, 5 (1973), pages 171-178, doi:10.1016/0012-365X(73)90108-8

Eric Weisstein's World of Mathematics, Triangle Graph

Wikipedia, Chromatic polynomial


Cf. A182797, A182788, A182789, A182790, A182791, A182792, A182793, A182794, A182795, A182796, A182798, A000217.

Sequence in context: A280477 A078535 A177781 * A183254 A143534 A104729

Adjacent sequences:  A178432 A178433 A178434 * A178436 A178437 A178438




Alois P. Heinz, Dec 21 2010



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Last modified December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)