Table 24 Magic topological formulas for clusters, continued
fcc truncated octahedron | |
Wiener | \(\frac {31813}{140}n^{7} + \frac {29741}{60}n^{6} + \frac {1925}{4}n^{5} + \frac {3259}{12}n^{4} + \frac {469}{5}n^{3}+\frac {281}{15}n^{2}+\frac {12}{7}n\) |
Reverse Wiener | \(\frac {39867}{140}n^{7} + \frac {27859}{60}n^{6} + \frac {1411}{4}n^{5} + \frac {1445}{12}n^{4} + \frac {41}{5}n^{3}-\frac {101}{15}n^{2}-\frac {12}{7}n\) |
HyperWiener | \(\frac {258927}{1120}n^{8}+\frac {115583}{168}n^{7} + \frac {211547}{240}n^{6} + \frac {19453}{30}n^{5} + \frac {144307}{480}n^{4} + \frac {2099}{24}n^{3}+\frac {12373}{840}n^{2}+\frac {39}{35}n\) |
Szeged | \(\frac {1120559}{1080}n^{9}+\frac {598387}{210}n^{8} + \frac {640481}{180}n^{7}+\frac {80023}{30}n^{6} + \frac {478073}{360}n^{5} + \frac {6677}{15}n^{4} + \frac {13388}{135}n^{3}+\frac {489}{35}n^{2}+\frac {16}{15}n\) |
bcc rhombic dodecahedron | |
Wiener | \(\frac {293}{35}n^{7} + \frac {293}{10}n^{6} + \frac {93}{2}n^{5} + 43n^{4} + \frac {721}{30}n^{3}+\frac {77}{10}n^{2}+\frac {23}{21}n\) |
Reverse Wiener | \(\frac {267}{35}n^{7} + \frac {187}{10}n^{6} + \frac {43}{2}n^{5} + 9n^{4} - \frac {61}{30}n^{3}-\frac {37}{10}n^{2}-\frac {23}{21}n\) |
HyperWiener | \(\frac {4187}{840}n^{8}+\frac {2533}{105}n^{7} + \frac {1011}{20}n^{6} + \frac {367}{6}n^{5} + \frac {5549}{120}n^{4} + \frac {647}{30}n^{3}+\frac {601}{105}n^{2}+\frac {9}{14}n\) |
Szeged | \(\frac {29447}{1890}n^{9}+\frac {110993}{1680}n^{8} + \frac {158141}{1260}n^{7}+\frac {16897}{120}n^{6} + \frac {18109}{180}n^{5} + \frac {10931}{240}n^{4} + \frac {23221}{1890}n^{3}+\frac {221}{140}n^{2}+\frac {2}{105}n\) |
Icosahedron | |
Wiener | \(\frac {118}{21}n^{7} + \frac {59}{3}n^{6} + \frac {97}{3}n^{5} + \frac {95}{3}n^{4} + \frac {55}{3}n^{3}+\frac {17}{3}n^{2}+\frac {5}{7}n\) |
Reverse Wiener | \(\frac {346}{63}n^{7} + \frac {41}{3}n^{6} + \frac {154}{9}n^{5} + \frac {25}{3}n^{4} + \frac {1}{9}n^{3}-2n^{2}-\frac {5}{7}n\) |
HyperWiener | \(\frac {311}{96}n^{8}+\frac {883}{56}n^{7} + \frac {1627}{48}n^{6} + 43n^{5} + \frac {3263}{96}n^{4} + \frac {127}{8}n^{3}+\frac {31}{8}n^{2}+\frac {5}{14}n\) |
Szeged | \(\frac {46049}{6048}n^{9}+\frac {46049}{1344}n^{8} + \frac {5521}{72}n^{7}+\frac {10415}{96}n^{6} + \frac {26417}{288}n^{5} + \frac {7303}{192}n^{4} + \frac {5735}{3024}n^{3}-\frac {1273}{336}n^{2}-\frac {11}{12}n\) |
Dodecahedron | |
Wiener | \(\frac {601}{7}n^{7} + \frac {601}{2}n^{6} + 416n^{5} + \frac {1155}{4}n^{4} + \frac {625}{6}n^{3}+\frac {71}{4}n^{2}+\frac {41}{42}n\) |
Reverse Wiener | \(\frac {799}{7}n^{7} + \frac {599}{2}n^{6} + 314n^{5} + \frac {605}{4}n^{4} + \frac {143}{6}n^{3}-\frac {15}{4}n^{2}-\frac {41}{42}n\) |
HyperWiener | \(\frac {2349}{28}n^{8}+\frac {757}{2}n^{7} + \frac {8203}{12}n^{6} + \frac {1267}{2}n^{5} + 321n^{4} + \frac {263}{3}n^{3}+\frac {242}{21}n^{2}+\frac {1}{3}n\) |
Szeged | \(\frac {1623611}{6048}n^{9}+\frac {1623611}{1344}n^{8} + \frac {1231255}{504}n^{7}+\frac {93211}{32}n^{6} + \frac {630167}{288}n^{5} + \frac {64439}{64}n^{4} + \frac {806507}{3024}n^{3}+\frac {14869}{336}n^{2}+\frac {487}{84}n\) |
Decahedron | |
Wiener | \(\frac {121}{504}n^{7} + \frac {121}{72}n^{6} + \frac {355}{72}n^{5} + \frac {565}{72}n^{4} + \frac {257}{36}n^{3}+\frac {125}{36}n^{2}+\frac {29}{42}n\) |
Reverse Wiener | \(\frac {229}{504}n^{7} + \frac {179}{72}n^{6} + \frac {415}{72}n^{5} + \frac {455}{72}n^{4} +\frac {89}{36}n^{3}-\frac {29}{36}n^{2}-\frac {29}{42}n\) |
HyperWiener | \(\frac {7}{72}n^{8}+\frac {905}{1008}n^{7} + \frac {499}{144}n^{6} + \frac {1055}{144}n^{5} + \frac {1327}{144}n^{4} + \frac {493}{72}n^{3}+\frac {49}{18}n^{2}+\frac {3}{7}n\) |
Szeged | \(\frac {9115}{72576}n^{9}+\frac {9115}{8064}n^{8} + \frac {54451}{12096}n^{7}+\frac {1999}{192}n^{6} + \frac {51751}{3456}n^{5} + \frac {4975}{384}n^{4} + \frac {26855}{4536}n^{3}+\frac {2021}{2016}n^{2}-\frac {11}{504}n\) |