#9136: more named graphs
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Reporter: mvngu | Owner: jason, ncohen, rlm
Type: enhancement | Status: new
Priority: major | Milestone: sage-wishlist
Component: graph theory | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Comment(by wdj):
The following at 3-regular Hamiltonian graphs, hence covered by the LCF
construction
(http://en.wikipedia.org/wiki/LCF_notation):
{{{
Balaban 10-cage
L = [-9, -25, -19, 29, 13, 35, -13, -29, 19, 25, 9, -29, 29, 17, 33, 21,
9,-13, -31, -9, 25, 17, 9, -31, 27, -9, 17, -19, -29, 27, -17, -9, -29,
33, -25,25, -21, 17, -17, 29, 35, -29, 17, -17, 21, -25, 25, -33, 29, 9,
17, -27, 29, 19, -17, 9, -27, 31, -9, -17, -25, 9, 31, 13, -9, -21, -33,
-17, -29, 29]
G = graphs.LCFGraph(70, L, 1)
Balaban 11-cage
L = [44, 26, -47, -15, 35, -39, 11, -27, 38, -37, 43, 14, 28, 51, -29,
-16, 41, -11, -26, 15, 22, -51, -35, 36, 52, -14, -33, -26, -46, 52, 26,
16, 43, 33, -15, 17, -53, 23, -42, -35, -28, 30, -22, 45, -44, 16, -38,
-16, 50, -55, 20, 28, -17, -43, 47, 34, -26, -41, 11, -36, -23, -16, 41,
17, -51, 26, -33, 47, 17, -11, -20, -30, 21, 29, 36, -43, -52, 10, 39,
-28, -17, -52, 51, 26, 37, -17, 10, -10, -45, -34, 17, -26, 27, -21, 46,
53, -10, 29, -50, 35, 15, -47, -29, -41, 26, 33, 55, -17, 42, -26, -36,
16]
G = graphs.LCFGraph(112, L, 1)
Bidiakis cube
G = graphs.LCFGraph(12, [6,4,-4], 4)
Biggs-Smith graph
L = [16, 24, -38, 17, 34, 48, -19, 41, -35, 47, -20, 34, -36, 21, 14, 48,
-16, -36, -43, 28, -17, 21, 29, -43, 46, -24, 28, -38, -14, -50, -45, 21,
8, 27, -21, 20, -37, 39, -34, -44, -8, 38, -21, 25, 15, -34, 18, -28, -41,
36, 8, -29, -21, -48, -28, -20, -47, 14, -8, -15, -27, 38, 24, -48, -18,
25, 38, 31, -25, 24, -46, -14, 28, 11, 21, 35, -39, 43, 36, -38, 14, 50,
43, 36, -11, -36, -24, 45, 8, 19, -25, 38, 20, -24, -14, -21, -8, 44, -31,
-38, -28, 37]
G = graphs.LCFGraph(102, L, 1)
Dyck graph
G = graphs.LCFGraph(32, [5,-5,13,-13], 8)
Foster graph
G = graphs.LCFGraph(90, [17,-9,37,-37,9,-17], 15)
Franklin graph
G = graphs.LCFGraph(12, [5,-5], 6)
Gray graph
G = graphs.LCFGraph(54, [-25,7,-7,13,-13,25], 9)
Harries graph
G = graphs.LCFGraph(70,
[-29,-19,-13,13,21,-27,27,33,-13,13,19,-21,-33,29], 5)
Harries-Wong graph
L = [9, 25, 31, -17, 17, 33, 9, -29, -15, -9, 9, 25, -25, 29, 17, -9, 9,
-27, 35, -9, 9, -17, 21, 27, -29, -9, -25, 13, 19, -9, -33, -17, 19, -31,
27, 11, -25, 29, -33, 13, -13, 21, -29, -21, 25, 9, -11, -19, 29, 9, -27,
-19, -13, -35, -9, 9, 17, 25, -9, 9, 27, -27, -21, 15, -9, 29, -29, 33,
-9, -25]
G = graphs.LCFGraph(70, L, 1)
Ljubljana graph
L = [47, -23, -31, 39, 25, -21, -31, -41, 25, 15, 29, -41, -19, 15, -49,
33, 39, -35, -21, 17, -33, 49, 41, 31, -15, -29, 41, 31, -15, -25, 21, 31,
-51, -25, 23, 9, -17, 51, 35, -29, 21, -51, -39, 33, -9, -51, 51, -47,
-33, 19, 51, -21, 29, 21, -31, -39]
G = graphs.LCFGraph(112, L, 2)
McGee graph
G = graphs.LCFGraph(24, [12,7,-7], 8)
Möbius–Kantor graph
G = graphs.LCFGraph(16, [5,-5], 8)
Nauru graph
G = graphs.LCFGraph(24, [5,-9,7,-7,9,-5], 4)
Tutte 12-cage
G = graphs.LCFGraph(126, [17, 27, -13, -59, -35, 35, -11, 13, -53, 53,
-27, 21, 57, 11, -21, -57, 59, -17], 7)
Tutte–Coxeter graph
G = graphs.LCFGraph(30, [-13,-9,7,-7,9,13], 5)
Wagner graph
G = graphs.LCFGraph(8, [4], 8)
}}}
Some of the Fullerene graphs can be expressed in LCF notation as well.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9136#comment:24>
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