Filter Moore graphs from an input string of whitespace-delimited graphs in graph6 format.

moore

#!/bin/bash

# Usage:
# echo `geng -qc 5` | moore.sh
#
# Note: Do not use for values greater than 6.

read g6raw
g6proc=$(echo $g6raw |
         awk '{  print "\"" $1 "\"" "," }' RS=' ' ORS=' ' |
         sed '$s/. $//')
g6list="["${g6proc}"]"

s="
load(graphs)$

moore1(G):=
 (
  K: max_degree(G)[1],
  k: min_degree(G)[1],
  d: diameter(G),
  g: girth(G),
  is_connected(G) and is(g = 2*d + 1 and k = K)
 )$

moore2(g):=
 (
  k: max_degree(g)[1],
  d: diameter(g),
  expected_order: 1 + k*(((k-1)^d - 1)/(k - 2)),
  is(graph_order(g) = expected_order)
 )$

moore3(g):=
 (
  k: min_degree(g)[1],
  d: (girth(g) - 1)/2,
  expected_order: 1 + k*(((k-1)^d - 1)/(k - 2)),
  is(graph_order(g) = expected_order)
 )$

g6list: $g6list$

glist: map(graph6_decode, g6list)$
moore_graphs: sublist(glist, moore1)$
map(graph6_encode, moore_graphs);
"

maxima --very-quiet --batch-string="$s"\
  | tail -n 1\
  | tr -d ' \t\r\f[]'\
  | tr ',' '\n'