On Matula numbers

Gutman, Iván; ctilde, Aleksandar Ivi

doi:10.1016/0012-365x(95)00182-v

Cited by 10 publications

(11 citation statements)

References 4 publications

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“…We would like to point out that some of the statistics we consider have been considered previously in [8], [10] and [13]. We include them here in order that the paper be self-contained (some of them play an auxiliary role at other statistics) and because our approach is slightly different.…”

Section: Statements and Proofsmentioning

confidence: 99%

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Rooted tree statistics from Matula numbers

Deutsch

2012

Discrete Applied Mathematics

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Section: Statements and Proofsmentioning

confidence: 99%

“…As pointed out by Ivan Gutman and Yeong-Nan Yeh [17], it is of interest to find statistics on rooted trees T directly from their Matula numbers µ(T ). This has been done for several statistics in [8], [10], [13].…”

Section: Introductionmentioning

confidence: 99%

Rooted tree statistics from Matula numbers

Deutsch

2012

Discrete Applied Mathematics

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“…A number of articles have been published on diverse correspondences and other relations between trees and natural numbers, such as [12], [13], [14], [15], [16], [17] and [18], but these studies do not focus specifically on binary trees.…”

Section: Introductionmentioning

confidence: 99%

A One-to-One Correspondence between Natural Numbers and Binary Trees

Skliar,

Gapper,

Monge

2020

Preprint

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A characterization is provided for each natural number except one (1) by means of an ordered pair of elements. The first element is a natural number called the type of the natural number characterized, and the second is a natural number called the order of the number characterized within those of its type. A one-to-one correspondence is specified between the set of binary trees such that a) a given node has no child nodes (that is, it is a terminal node), or b) it has exactly two child nodes. Thus, binary trees such that one of their parent nodes has only one child node are excluded from the set considered here.

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“…of a rooted tree that can be obtained directly from the associated Matula number. Three years later, Gutman and Ivić [9] proved that for n ≥ 5, the rooted tree obtained by taking a root path (rooted at one of its endvertices) on n − 3 vertices and attaching three leaves to the other endvertex of the path, is the one that has the maximal Matula number over the set of all rooted trees with n vertices. For the minimum, they showed that for n ≥ 3 and depending on the residue class of n modulo 3, the rooted tree depicted in Figure 2 is minimal among all n-vertex rooted trees.…”

Section: Introductionmentioning

confidence: 99%

The topological trees with extreme Matula numbers

Dossou-Olory

2018

Preprint

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Let T be a rooted tree with branches T 1 , T 2 , . . . , T r and p m the m-th prime number (p 1 = 2, p 2 = 3, p 3 = 5, . . .). The Matula number M (T ) of T is p M (T1) •p M (T2) •. . .• p M (Tr) , starting with M (•) = 1. It was put forward half a century ago by the American mathematician David Matula. In this paper, we prove that the star (consisting of a root and leaves attached to it) and the binary caterpillar (a binary tree whose internal vertices form a path starting at the root) have the smallest and greatest Matula number, respectively, over all topological trees (rooted trees without vertices of outdegree 1) with a prescribed number of leaves -the extremal values are also derived.

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On Matula numbers

Cited by 10 publications

References 4 publications

Rooted tree statistics from Matula numbers

Rooted tree statistics from Matula numbers

A One-to-One Correspondence between Natural Numbers and Binary Trees

The topological trees with extreme Matula numbers

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