

A235112


a(n) = the largest of the Mindices of the trees with n vertices.


1



1, 2, 3, 7, 16, 32, 64, 152, 361, 1273, 4489, 22177, 109561, 735151
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

We define the Mindex of a tree T to be the smallest of the Matula numbers of the rooted trees isomorphic (as a tree) to T. Example. The path tree P[5] = ABCDE has Mindex 9. Indeed, there are 3 rooted trees isomorphic to P[5]: rooted at A, B, and C, respectively. Their Matula numbers are 11, 10, and 9, respectively. Consequently, the Mindex of P[5] is 9.
a(n) = largest (= last) entry in row n of A235111.
It is conjectured that for n>=7 one has a(n) = A235120(n6).
These numbers can be useful, for example, in the following situation. We intend to identify all trees that have 10 vertices and satisfy a certain property. Instead of scanning all rooted trees with Matula numbers from A005517(10)=125 to A005518(10)=219613, we do the scanning only for Matula numbers between 125 and a(10)=1273.


LINKS

Table of n, a(n) for n=1..14.
E. Deutsch, Tree statistics from Matula numbers, arXiv preprint arXiv:1111.4288, 2011.
E. Deutsch, Rooted tree statistics from Matula numbers, Discrete Appl. Math., 160, 2012, 23142322.
F. Goebel, On a 11correspondence between rooted trees and natural numbers, J. Combin. Theory, B 29 (1980), 141143.
I. Gutman and A. Ivic, On Matula numbers, Discrete Math., 150, 1996, 131142.
I. Gutman and YeongNan Yeh, Deducing properties of trees from their Matula numbers, Publ. Inst. Math., 53 (67), 1993, 1722.
I. Gutman, W. Linert, I. Lukovits, and Z. Tomovic, The multiplicative version of the Wiener index, J. Chem. Inf. Comput. Sci., 40, 2000, 113116.
I. Gutman, W. Linert, I. Lukovits, and Z. Tomovic, On the multiplicative Wiener index and its possible chemical applications, Monatshefte f. Chemie, 131, 2000, 421427.
D. W. Matula, A natural rooted tree enumeration by prime factorization, SIAM Rev. 10 (1968) 273.
Index entries for sequences related to MatulaGoebel numbers


FORMULA

a(n) = A235111(n,A000055(n)).


EXAMPLE

a(4)=7. Indeed, there are 2 trees with 4 vertices: the path P[4] and the star S[3] with 3 edges. There are two rooted trees isomorphic to P[4]; they have Matula numbers 5 and 6; so the Mindex is 5. There are two rooted trees isomorphic to S[3]; they have Matula numbers 7 and 8; so the Mindex is 7. Max(5,7) = 7.


CROSSREFS

Cf. A235111, A005518.
Sequence in context: A049956 A289844 A153056 * A081207 A334398 A027118
Adjacent sequences: A235109 A235110 A235111 * A235113 A235114 A235115


KEYWORD

nonn,more


AUTHOR

Emeric Deutsch, Jan 03 2014


EXTENSIONS

a(13) from Emeric Deutsch, Feb 16 2014
a(14) from Emeric Deutsch, Mar 12 2014


STATUS

approved



