GraphBank

Random sample from database

Basic information
ID
Name Cayley Graph of k = 3
Description New record of Degree/Diameter problem on Dec. 2017, compared to the graph of Loz and Pineda-Villavicencio (2009, order 1620 for degree 18). Cayley Graph. Order 1638, Degree 18, Diameter 3. Group (m, n, r) = (91, 18, 3). Quotient B(0, 9) Voltages [(2, 11)(21, 5)(27, 2)(29, 7)(33, 13)(41, 10)(43, 2)(43, 16)(44, 15)] Reference: E. Loz and G. Pineda-Villavicencio, "New Benchmarks for Large-Scale Networks with Given Maximum Degree and Diameter," The Computer Journal, vol.53, no.7, pp.1092-1105, Sep. 2010. https://doi.org/10.1093/comjnl/bxp091
Submitted by
Date2017-12-07 11:48
Download link
Features
Vertices 1638
Edges 14742
Regular
Maximum degree 18
Diameter 3
Connected
Average path length 2.79108124618204

Other Solutions

1303 (18,3)-graph with 1620 vertices 1620 18 3 graphbank 2016-11-28 03:41
1345 (17,3)-graph with 1610 vertices 1610 17 3 graphbank 2016-11-28 03:41
1273 (16,3)-graph with 1600 vertices 1600 16 3 graphbank 2016-11-28 03:41
1301 (15,3)-graph with 1215 vertices 1215 15 3 graphbank 2016-11-28 03:41
1408 (14,3)-graph with 916 vertices 916 14 3 graphbank 2016-11-28 03:41
1358 (13,3)-graph with 851 vertices 851 13 3 graphbank 2016-11-28 03:41
1292 (12,3)-graph with 786 vertices 786 12 3 graphbank 2016-11-28 03:41
1402 (11,3)-graph with 715 vertices 715 11 3 graphbank 2016-11-28 03:41
1351 (10,3)-graph with 650 vertices 650 10 3 graphbank 2016-11-28 03:41
1302 (9,3)-graph with 585 vertices 585 9 3 graphbank 2016-11-28 03:41