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

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

Offset: 0

Author

N. J. A. Sloane, Jul 01 2018

Keywords

• nonn
• fini
• full

Comments

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

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.

Links

• A. T. Balaban, A trivalent graph of girth ten, Journal of Combinatorial Theory Series B 12 (1972), 1-5.
• M. R. O'Keefe and P. K. Wong, A smallest graph of girth 10 and valency 3, Journal of Combinatorial Theory Series B 29 (1980), 91-105.
• N. J. A. Sloane, Balaban's 10-cage, 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.
• N. J. A. Sloane, Coordination sequence for a node of type A
• N. J. A. Sloane, Coordination sequence for a node of type B
• N. J. A. Sloane, Coordination sequence for a node of type C
• Eric Weisstein's World of Mathematics, Balaban 10-cage
• Wikipedia, Balaban 10-cage

Crossrefs

See A250120 for links to thousands of other coordination sequences.