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

Damir Vukičević, Sarah Rajtmajer, Nenad Trinajstić

Research output: Contribution to journalArticle

29 Citations (Scopus)

### 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 n 1 , 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 Δ 3 , 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) 65-70 6 Match 60 1 Published - Jul 10 2008

### Fingerprint

Zagreb Index
Edge-connectivity
Time Constant
Directly proportional
Molecules
Output

### All Science Journal Classification (ASJC) codes

• Chemistry(all)
• Computer Science Applications
• Computational Theory and Mathematics
• Applied Mathematics

### Cite this

Vukičević, Damir ; Rajtmajer, Sarah ; Trinajstić, Nenad. / Trees with maximal second Zagreb index and prescribed number of vertices of the given degree. In: Match. 2008 ; Vol. 60, No. 1. pp. 65-70.
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Trees with maximal second Zagreb index and prescribed number of vertices of the given degree. / Vukičević, Damir; Rajtmajer, Sarah; Trinajstić, Nenad.

In: Match, Vol. 60, No. 1, 10.07.2008, p. 65-70.

Research output: Contribution to journalArticle

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