> #Attendence Q1. ; > #Who invented Latin squares and Latin-Greco squares, and what are there? ; > #Leonhard Euler. In combinatorics and in experimental design, a Latin square is an n × n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column. ; > ; > #Attendence Q2. ; > #What is nops(AllGraphs(20)) ; > #for nops(AllGraphs(n)), ; > #n=4->2^6 ; > #n=5->2^10 ; > #n=6->2^15 ; > #n=7->2^21 ; > #By conjecture, nops(AllGraphs(20)) = 2^(1+2+...+19) = 2^190 ; > ; > #Attendence Q3. ; > #What is CC(G,38)? ; > G:=RandGr(200,50) Typesetting:-mprintslash([(G := [{}, {44}, {}, {}, {137}, {}, {}, {}, {}, {}, { 125, 144}, {66}, {53, 61}, {}, {}, {}, {}, {}, {139}, {}, {}, {66}, {198}, {}, {}, {}, {}, {}, {}, {}, {131}, {}, {}, {}, {}, {}, {}, {131}, {}, {}, {}, {192} , {}, {2}, {}, {}, {}, {}, {}, {}, {}, {169}, {13, 89}, {}, {182}, {}, {}, {}, {}, {130}, {13}, {}, {165}, {}, {}, {12, 22}, {}, {72, 75, 145}, {}, {158}, {}, {68, 128}, {}, {}, {68, 178, 189}, {138, 180}, {}, {}, {}, {172}, {}, {131}, {} , {157}, {}, {111, 143, 153}, {}, {}, {53, 132, 141}, {130}, {}, {}, {}, {}, {} , {}, {}, {168}, {}, {167}, {129}, {}, {138}, {}, {141}, {}, {}, {}, {}, {116}, {86}, {}, {146, 155}, {}, {}, {110}, {}, {}, {}, {}, {}, {}, {}, {130, 156}, { 11}, {}, {}, {72}, {101}, {60, 90, 124}, {31, 38, 82}, {89}, {}, {}, {}, {}, {5 }, {76, 103}, {19}, {167}, {89, 105}, {}, {86}, {11, 152}, {68}, {113}, {177}, {}, {}, {}, {}, {144}, {86}, {}, {113}, {124, 172}, {84}, {70}, {}, {}, {}, {}, {}, {}, {63}, {}, {100, 140}, {98}, {52}, {}, {}, {80, 156}, {}, {}, {}, {}, { 147}, {75}, {}, {76}, {}, {55}, {}, {}, {}, {}, {}, {}, {75}, {}, {}, {42}, {}, {}, {}, {}, {}, {23}, {}, {}])],[[{}, {44}, {}, {}, {137}, {}, {}, {}, {}, {}, {125, 144}, {66}, {53, 61}, {}, {}, {}, {}, {}, {139}, {}, {}, {66}, {198}, {}, {}, {}, {}, {}, {}, {}, {131}, {}, {}, {}, {}, {}, {}, {131}, {}, {}, {}, {192} , {}, {2}, {}, {}, {}, {}, {}, {}, {}, {169}, {13, 89}, {}, {182}, {}, {}, {}, {}, {130}, {13}, {}, {165}, {}, {}, {12, 22}, {}, {72, 75, 145}, {}, {158}, {}, {68, 128}, {}, {}, {68, 178, 189}, {138, 180}, {}, {}, {}, {172}, {}, {131}, {} , {157}, {}, {111, 143, 153}, {}, {}, {53, 132, 141}, {130}, {}, {}, {}, {}, {} , {}, {}, {168}, {}, {167}, {129}, {}, {138}, {}, {141}, {}, {}, {}, {}, {116}, {86}, {}, {146, 155}, {}, {}, {110}, {}, {}, {}, {}, {}, {}, {}, {130, 156}, { 11}, {}, {}, {72}, {101}, {60, 90, 124}, {31, 38, 82}, {89}, {}, {}, {}, {}, {5 }, {76, 103}, {19}, {167}, {89, 105}, {}, {86}, {11, 152}, {68}, {113}, {177}, {}, {}, {}, {}, {144}, {86}, {}, {113}, {124, 172}, {84}, {70}, {}, {}, {}, {}, {}, {}, {63}, {}, {100, 140}, {98}, {52}, {}, {}, {80, 156}, {}, {}, {}, {}, { 147}, {75}, {}, {76}, {}, {55}, {}, {}, {}, {}, {}, {}, {75}, {}, {}, {42}, {}, {}, {}, {}, {}, {23}, {}, {}]]) ; > CC(G,38) {31, 38, 82, 131} ; > ; > #Attendence Q4. ; > #Is this sequence in the OEIS? If it is, what is the A-number? ; > #Yes. A1187: Number of connected labeled graphs with n nodes. ; > ; > #Attendence Q5: > #Draw this graph manully ; > # 8-1-4-6-9-3-5-7-10-2-5 ; > ; > #Attendence Q6: > #Is this sequence in the OEIS? A-number? ; > #A272: Number of trees on n labeled nodes: n^(n-2) with a(0)=1. ; > ; > #Attendence Q7: > #Is this in the oeis? What is the A-number? ; > #A57500: Number of connected labeled graphs with n edges and n nodes. ; > ;