

A058227


Number of edges in all simple (loopless) paths, connecting any node with all the remaining ones in optimal graphs degree 4.


0




OFFSET

1,1


COMMENTS

Number of edges occurring in all simple, loopless paths, connecting any node with all the remaining ones forming optimal graphs degree 4,(2*d(G)^2+2*d(G)+1,2*d(G)+1); d(G)  graph diameter


REFERENCES

Concrete Mathematics  R. L. Graham, D.E. Knuth, O. Patashnik, 1994 AddisonWesley company, Inc.


LINKS

Table of n, a(n) for n=1..8.


FORMULA

a(n)=d(V)*Sum('n*(2^n1)', 'n'=1..d(G)); d(V) graph degree, d(G)  diameter a(n)=d(V)*array(1..d(G))*array(1..(2^d(G)1));


EXAMPLE

a(5)=4(1+2*3+3*7+4*15+5*31)=972 S := array(1..5,[1,2,3,4,5]); T := array(1..5,[1,3,7,15,31]); a(5) := evalm(S&*T); a(5) := 243


MAPLE

d(V) := 4; n := 5; a(n) := d(V)*sum('n*(2^n1)', 'n'=1..n); or d(V) := 4; S := array(1..5, [1, 2, 3, 4, 5]); T := array(1..5, [1, 3, 7, 15, 31]); a(5) := d(V)*evalm(S&*T);


CROSSREFS

Sequence in context: A092712 A202964 A183469 * A296392 A318011 A328685
Adjacent sequences: A058224 A058225 A058226 * A058228 A058229 A058230


KEYWORD

nonn


AUTHOR

S. Bujnowski (slawb(AT)atr.bydgoszcz.pl), Feb 13 2002


STATUS

approved



