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A316318 Coordination sequence for a node in the graph of Balaban's (3,10)-cage.

%I A316318 #42 Jun 25 2025 03:33:42
%S A316318 1,3,6,12,24,20,4
%N A316318 Coordination sequence for a node in the graph of Balaban's (3,10)-cage.
%C A316318 The graph has 70 nodes, 105 edges, degree 3, girth 10 and diameter 6.
%C A316318 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 A316318 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 A316318 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 A316318 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 A316318 N. J. A. Sloane, <a href="/A316318/a316318_5.png">Coordination sequence for a node of type A</a>
%H A316318 N. J. A. Sloane, <a href="/A316318/a316318_6.png">Coordination sequence for a node of type B</a>
%H A316318 N. J. A. Sloane, <a href="/A316318/a316318_7.png">Coordination sequence for a node of type C</a>
%H A316318 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Balaban10-Cage.html">Balaban 10-cage</a>
%H A316318 Wikipedia, <a href="https://en.wikipedia.org/wiki/Balaban_10-cage">Balaban 10-cage</a>
%Y A316318 See A250120 for links to thousands of other coordination sequences.
%K A316318 nonn,fini,full
%O A316318 0,2
%A A316318 _N. J. A. Sloane_, Jul 01 2018