;; GRAPHS.LISP
;; some CM graphs from group theory

;; Drew Krause, 2004
;; drkrause@mindspring.com
;; www.wordecho.org

;; D4-GRAPH: dihedral group (4) -- size 4
(define d4-graph (new graph of
		      `((a :id 1 :to ,(new random of '(2 3)))
			(b :id 2 :to ,(new random of '(1 4)))
			(c :id 3 :to ,(new random of '(1 4)))
			(d :id 4 :to ,(new random of '(2 3))))))

;; TRANS8C-GRAPH: transitive group (8) id 3 -- size 8
(define trans8c-graph (new graph of
			   `((a :id 1 :to ,(new random of '(3 5 8)))
			     (b :id 2 :to ,(new random of '(3 6 8)))
			     (c :id 3 :to ,(new random of '(1 2 7)))
			     (d :id 4 :to ,(new random of '(5 6 8)))
			     (e :id 5 :to ,(new random of '(1 4 7)))
			     (f :id 6 :to ,(new random of '(2 4 7)))
			     (g :id 7 :to ,(new random of '(3 5 6)))
			     (h :id 8 :to ,(new random of '(1 2 4))))))

;; TRANS6A-GRAPH: transitive group (6) id 1 -- size 6
;; "kinda cyclic"
(define trans6a-graph (new graph of
			   `((a :id 1 :to ,(new random of '(2 6)))
			     (b :id 2 :to ,(new random of '(1 3)))
			     (c :id 3 :to ,(new random of '(2 4)))
			     (d :id 4 :to ,(new random of '(3 5)))
			     (e :id 5 :to ,(new random of '(4 6)))
			     (f :id 6 :to ,(new random of '(1 5))))))

;; TRANS6B-GRAPH: transitive group (6) id 2 -- size 6
;; "no steps"
(define trans6b-graph (new graph of
			   `((a :id 1 :to ,(new random of '(3 4 5)))
			     (b :id 2 :to ,(new random of '(4 5 6)))
			     (c :id 3 :to ,(new random of '(1 5 6)))
			     (d :id 4 :to ,(new random of '(1 2 6)))
			     (e :id 5 :to ,(new random of '(1 2 3)))
			     (f :id 6 :to ,(new random of '(2 3 4))))))

;; TRANS6C-GRAPH: transitive group (6) id 3 --- size 12
(define trans6c-graph (new graph of
		      `((a :id 1 :to ,(new random of '(4 7 11)))
			(b :id 2 :to ,(new random of '(3 8 12)))
			(c :id 3 :to ,(new random of '(2 5 10)))
			(d :id 4 :to ,(new random of '(1 6 9)))
			(e :id 5 :to ,(new random of '(3 7 11)))
			(f :id 6 :to ,(new random of '(4 8 12)))
			(g :id 7 :to ,(new random of '(1 5 9)))
			(h :id 8 :to ,(new random of '(2 6 10)))
			(i :id 9 :to ,(new random of '(4 7 12)))
			(j :id 10 :to ,(new random of '(3 8 11)))
			(k :id 11 :to ,(new random of '(1 5 10)))
			(l :id 12 :to ,(new random of '(2 6 9))))))

;; SMALL12A-GRAPH: small group (12) id 1 --- size 12
(define small12a-graph (new graph of
		      `((a :id 1 :to ,(new random of '(2 3 4 5 8)))
			(b :id 2 :to ,(new random of '(1 3 5 6 10)))
			(c :id 3 :to ,(new random of '(1 2 5 7 11)))
			(d :id 4 :to ,(new random of '(1 6 7 8 9)))
			(e :id 5 :to ,(new random of '(1 2 3 9 12)))
			(f :id 6 :to ,(new random of '(2 4 7 9 10)))
			(g :id 7 :to ,(new random of '(3 4 6 9 11)))
			(h :id 8 :to ,(new random of '(1 4 10 11 12)))
			(i :id 9 :to ,(new random of '(4 5 6 7 12)))
			(j :id 10 :to ,(new random of '(2 6 8 11 12)))
			(k :id 11 :to ,(new random of '(3 7 8 10 12)))
			(l :id 12 :to ,(new random of '(5 8 9 10 11))))))

;; SMALL12B-GRAPH: small group (12) id 2 --- size 12
(define small12b-graph (new graph of
		      `((a :id 1 :to ,(new random of '(2 3 4 6 7)))
			(b :id 2 :to ,(new random of '(1 4 5 6 9)))
			(c :id 3 :to ,(new random of '(1 5 7 8 10)))
			(d :id 4 :to ,(new random of '(1 2 6 8 11)))
			(e :id 5 :to ,(new random of '(2 3 8 9 10)))
			(f :id 6 :to ,(new random of '(1 2 4 10 12)))
			(g :id 7 :to ,(new random of '(1 3 9 11 12)))
			(h :id 8 :to ,(new random of '(3 4 5 10 11)))
			(i :id 9 :to ,(new random of '(2 5 7 11 12)))
			(j :id 10 :to ,(new random of '(3 5 6 8 12)))
			(k :id 11 :to ,(new random of '(4 7 8 9 12)))
			(l :id 12 :to ,(new random of '(6 7 9 10 11))))))

;; ALT4-GRAPH: alternating group (4) --- size 12
(define alt4-graph (new graph of
		      `((a :id 1 :to ,(new random of '(2 3 5 7)))
			(b :id 2 :to ,(new random of '(1 3 9 10)))
			(c :id 3 :to ,(new random of '(1 2 4 11)))
			(d :id 4 :to ,(new random of '(3 5 6 11)))
			(e :id 5 :to ,(new random of '(1 4 6 7)))
			(f :id 6 :to ,(new random of '(4 5 8 0)))
			(g :id 7 :to ,(new random of '(1 5 8 9)))
			(h :id 8 :to ,(new random of '(6 7 9 0)))
			(i :id 9 :to ,(new random of '(2 7 8 10)))
			(j :id 10 :to ,(new random of '(2 9 11 0)))
			(k :id 11 :to ,(new random of '(3 4 10 0)))
			(l :id 0 :to ,(new random of '(6 8 10 11))))))