A316318 - OEIS

%I #39 Jul 01 2018 18:43:07

%S 1,3,6,12,24,20,4

%N Coordination sequence for a node in the graph of Balaban's (3,10)-cage.

%C The graph has 70 nodes, 105 edges, degree 3, girth 10 and diameter 6.

%C The automorphism group of this graph has order 80, and has three orbits on nodes, of sizes 40, 20, and 10, respectively. However, the coordination sequence is independent of the choice of the node.

%H A. T. Balaban, <a href="https://doi.org/10.1016/0095-8956(72)90028-7">A trivalent graph of girth ten</a>, Journal of Combinatorial Theory Series B 12 (1972), 1-5.

%H M. R. O'Keefe and P. K. Wong, <a href="https://doi.org/10.1016/0095-8956(72)90028-7">A smallest graph of girth 10 and valency 3</a>, Journal of Combinatorial Theory Series B 29 (1980), 91-105.

%H N. J. A. Sloane, <a href="/A316318/a316318_1.png">Balaban's 10-cage</a>, showing 4 disjoint decagons (blue, red, green, yellow) and the three types (A, B, C) of nodes. The labels A, B, C are the same as in Fig. 2 of Balaban's 1972 article.

%H N. J. A. Sloane, <a href="/A316318/a316318_5.png">Coordination sequence for a node of type A</a>

%H N. J. A. Sloane, <a href="/A316318/a316318_6.png">Coordination sequence for a node of type B</a>

%H N. J. A. Sloane, <a href="/A316318/a316318_7.png">Coordination sequence for a node of type C</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Balaban10-Cage.html">Balaban 10-cage</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Balaban_10-cage">Balaban 10-cage</a> [Note that as of Jul 01 2018 this page contains errors. For example, M. R. O'Keefe and P. K. Wong (1980) only assert that there at least three (3,10)-cages. Weisstein's discussion is more accurate.  - _N. J. A. Sloane_, Jul 01 2018]

%Y See A250120 for links to thousands of other coordination sequences.

%K nonn,fini,full

%O 0,2

%A _N. J. A. Sloane_, Jul 01 2018