A072249 a(n) is the least k such that for every m >= k, the characteristic set of the lollipop graph C_{m,n} is the central edge of its pendant path.

5, 7, 11, 17, 21, 27, 35, 41

Offset

3,1

Comments

From Bartlomiej Pawlik, Jun 17 2026: (Start)

The lollipop graph C_{m,n} is the unicyclic graph on m vertices obtained by joining a cycle of length n to an endpoint of a path on m-n+1 vertices.

The characteristic set of a graph with respect to a Fiedler vector consists of the vertices at which the vector is zero and the edges whose endpoints have values of opposite signs.

More precisely, a(n) is the least k such that, for every m >= k, the characteristic set of C_{m,n}, labeled as in Fig. 9 of Fallat, Kirkland and Pati, is the single edge [ceiling(m/2), ceiling(m/2)+1]. (End)

Links

Table of n, a(n) for n=3..10.

S. M. Fallat, S. Kirkland and S. Pati, Minimizing algebraic connectivity over connected graphs with fixed girth, Discr. Math., 254 (2002), 115-142.

Formula

a(n) <= floor((-3 + sqrt(16*Pi^2*n*(n - 1)^2 + 10))/8) + 1. - Bartlomiej Pawlik, Jun 17 2026

Crossrefs

Sequence in context: A386133 A271658 A282739 * A076665 A124598 A096215

Adjacent sequences: A072246 A072247 A072248 * A072250 A072251 A072252

Keyword

nonn,more

Author

N. J. A. Sloane, Jul 06 2002

Extensions

Name clarified by Bartlomiej Pawlik, Jun 17 2026

Status

approved