Trees with maximal second Zagreb index and prescribed number of vertices of the given degree

Damir Vukičević; Sarah Michele Rajtmajer; Nenad Trinajstić

Trees with maximal second Zagreb index and prescribed number of vertices of the given degree

Damir Vukičević
, Sarah Michele Rajtmajer
, Nenad Trinajstić

College of Information Sciences and Technology

Research output: Contribution to journal › Article › peer-review

31 Scopus citations

Abstract

In this paper we present a simple algorithm for calculating the maximal value of the second Zagreb index for trees with prescribed number of vertices of given degree. The user needs only to input values n₁, n ₂,...,n_δ where n_i is the number of vertices of degree i. The algorithm outputs the edge connectivity values m _ij as well as the maximal value of the second Zagreb index. The complexity of the algorithm is proportional to Δ³, where Δ is maximal degree. Since complexity is independent of the number of vertices, for chemical trees that have Δ ≤ 4 the algorithm works in constant time no matter how large the molecule is.

Original language	English (US)
Pages (from-to)	65-70
Number of pages	6
Journal	Match
Volume	60
Issue number	1
State	Published - 2008

All Science Journal Classification (ASJC) codes

General Chemistry
Computer Science Applications
Computational Theory and Mathematics
Applied Mathematics

Cite this

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abstract = "In this paper we present a simple algorithm for calculating the maximal value of the second Zagreb index for trees with prescribed number of vertices of given degree. The user needs only to input values n1, n 2,...,nδ where ni is the number of vertices of degree i. The algorithm outputs the edge connectivity values m ij as well as the maximal value of the second Zagreb index. The complexity of the algorithm is proportional to Δ3, where Δ is maximal degree. Since complexity is independent of the number of vertices, for chemical trees that have Δ ≤ 4 the algorithm works in constant time no matter how large the molecule is.",

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AU - Vukičević, Damir

AU - Rajtmajer, Sarah Michele

AU - Trinajstić, Nenad

PY - 2008

Y1 - 2008

N2 - In this paper we present a simple algorithm for calculating the maximal value of the second Zagreb index for trees with prescribed number of vertices of given degree. The user needs only to input values n1, n 2,...,nδ where ni is the number of vertices of degree i. The algorithm outputs the edge connectivity values m ij as well as the maximal value of the second Zagreb index. The complexity of the algorithm is proportional to Δ3, where Δ is maximal degree. Since complexity is independent of the number of vertices, for chemical trees that have Δ ≤ 4 the algorithm works in constant time no matter how large the molecule is.

AB - In this paper we present a simple algorithm for calculating the maximal value of the second Zagreb index for trees with prescribed number of vertices of given degree. The user needs only to input values n1, n 2,...,nδ where ni is the number of vertices of degree i. The algorithm outputs the edge connectivity values m ij as well as the maximal value of the second Zagreb index. The complexity of the algorithm is proportional to Δ3, where Δ is maximal degree. Since complexity is independent of the number of vertices, for chemical trees that have Δ ≤ 4 the algorithm works in constant time no matter how large the molecule is.

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ER -

Trees with maximal second Zagreb index and prescribed number of vertices of the given degree

Abstract

All Science Journal Classification (ASJC) codes

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