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

29 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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AU - Trinajstić, Nenad

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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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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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