A217246 - OEIS

%I #32 Feb 16 2025 08:33:18

%S 1,1,0,1,0,1,0,3,3,13,21,110,474,2545,18696,136749,1447003,18772435,

%T 303050079,6239596472

%N Number of highly irregular connected graphs with n nodes.

%C A connected graph is highly irregular if the neighbors of each vertex have distinct degrees. Such graphs exist on all orders except 3, 5 and 7. [from the McKay link]

%H Avraham Itzhakov and Michael Codish, <a href="http://arxiv.org/abs/1511.08205">Breaking Symmetries in Graph Search with Canonizing Sets</a>, arXiv:1511.08205 [cs.AI], 2015-2016.

%H Brendan McKay, <a href="http://users.cecs.anu.edu.au/~bdm/data/graphs.html">Combinatorial Data</a> (on graphs); see bottom of page.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HighlyIrregularGraph.html">Highly Irregular Graph</a>

%e a(4) = 1, the only such graph is the linear graph: o--o--o--o

%K more,nonn

%O 1,8

%A _Joerg Arndt_, Mar 16 2013

%E a(16)-a(19) from _Michael Codish_, Dec 01 2015

%E a(20) from _Michael Codish_, Jan 17 2016