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A206484
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Numerator of the complexity index B of the path graph on n vertices (n>=2).
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1
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2, 5, 4, 116, 466, 895, 2011, 11887, 456586, 4673247, 3737, 4105421072, 84949477486, 25869451, 330137431, 7982039918, 726807741125074, 2180011073659, 144755460533, 772879344134036, 193884856434901466474, 324829874191095862, 70339720614511, 184390793325658393
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OFFSET
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2,1
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COMMENTS
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The complexity index B of a graph G is defined as Sum(a[i]/d[i]), where a[i] is the degree of the vertex i and d[i] is the distance degree of i (the sum of distances from i to all the vertices of G), the summation being over all the vertices of G (see the Bonchev & Buck reference, p. 215).
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REFERENCES
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D. Bonchev and G. A. Buck, Quantitative measures of network complexity, in: Complexity in Chemistry, Biology, and Ecology, Springer, New York, pp. 191-235.
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LINKS
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FORMULA
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The complexity index B of the path on n vertices is 4*(Sum_{j=1..n} 1/(n*(n + 1 - 2*j) + 2*j*(j-1))) - 4/(n*(n-1)).
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EXAMPLE
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a(3)=5 because the vertices of the path ABC have degrees 1, 2, 1 and distance degrees 3, 2, 3; then 1/3 + 2/2 + 1/3 = 5/3.
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MAPLE
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a := proc (n) options operator, arrow: numer(4*(sum(1/(n*(n+1-2*j)+2*j*(j-1)), j = 1 .. n))-4/(n*(n-1))) end proc: seq(a(n), n = 2 .. 25);
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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