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A228598
The Wiener index of the graph obtained by applying Mycielski's construction to the crown graph G(n) (n>=3).
0
141, 240, 365, 516, 693, 896, 1125, 1380, 1661, 1968, 2301, 2660, 3045, 3456, 3893, 4356, 4845, 5360, 5901, 6468, 7061, 7680, 8325, 8996, 9693, 10416, 11165, 11940, 12741, 13568, 14421, 15300, 16205, 17136, 18093, 19076, 20085, 21120
OFFSET
3,1
COMMENTS
The crown graph G(n) is the graph with vertex set {x(1), x(2), ...x(n), y(1), y(2), ..., y(n)} and edge set {(x(i), y(j)): 1<=i,j<=n, i != j} (= the complete bipartite graph K(n,n) with horizontal edges removed).
The value a(4)=240 has been checked by the direct computation of the distance matrix of the Mycielskian of G(4) (via Maple).
REFERENCES
D. B. West, Introduction to Graph Theory, 2nd ed., Prentice-Hall, NJ, 2001, p. 205.
LINKS
R. Balakrishnan, S. F. Raj, The Wiener number of powers of the Mycielskian, Discussiones Math. Graph Theory, 30, 2010, 489-498 (see Theorem 2.1).
B. E. Sagan, Y-N. Yeh and P. Zhang, The Wiener Polynomial of a Graph, Internat. J. of Quantum Chem., 60, 1996, 959-969.
FORMULA
a(n) = 13*n^2 + 8*n.
G.f.: x^3*(141-183*x+68*x^2)/(1-x)^3.
MAPLE
a := proc (n) options operator, arrow: 13*n^2+8*n end proc: seq(a(n), n = 3 .. 40);
PROG
(PARI) a(n)=13*n^2+8*n \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Cf. A033428.
Sequence in context: A208179 A368670 A045936 * A031892 A063373 A145192
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Aug 29 2013
STATUS
approved