A060202 - OEIS

A060202

Let G = complete graph on 4 vertices, create the sequence G, L(G), L(L(G)), L(L(L(G))), ... where each graph in this sequence is the line graph of the previous graph; a(n) is number of vertices of the n-th graph in this sequence.

%I #5 May 10 2013 12:44:36

%S 4,6,12,36,180,1620,27540,908820,59073300,7620455700,1958457114900,

%T 1004688499943700,1029805712442292500,2110071904794257332500,

%U 8644964593942072291252500,70828194918167398282231732500

%N Let G = complete graph on 4 vertices, create the sequence G, L(G), L(L(G)), L(L(L(G))), ... where each graph in this sequence is the line graph of the previous graph; a(n) is number of vertices of the n-th graph in this sequence.

%C If G is k-regular, then L(G) is (2k-2)-regular. From this it is easy to get the formula for a(n).

%F a(0)=4 and for n >= 1 a(n) = 4 * product k=1...n (1+2^(k-2))

%e The line graph of the complete graph on 4 vertices has C(4,2) vertices so a(1) = 6.

%p for n from 0 to 30 do printf(`%d,`,4*product(1+2^(k-2), k=1..n)) od:

%K nonn

%O 0,1

%A Avi Peretz (njk(AT)netvision.net.il), Mar 18 2001

%E More terms from _James A. Sellers_ and _Vladeta Jovovic_, Mar 26 2001