### 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) |
---|---|

Pages (from-to) | 65-70 |

Number of pages | 6 |

Journal | Match |

Volume | 60 |

Issue number | 1 |

State | Published - Jul 10 2008 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Match*,

*60*(1), 65-70.

}

*Match*, vol. 60, no. 1, pp. 65-70.

**Trees with maximal second Zagreb index and prescribed number of vertices of the given degree.** / Vukičević, Damir; Rajtmajer, Sarah; Trinajstić, Nenad.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Trees with maximal second Zagreb index and prescribed number of vertices of the given degree

AU - Vukičević, Damir

AU - Rajtmajer, Sarah

AU - Trinajstić, Nenad

PY - 2008/7/10

Y1 - 2008/7/10

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 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.

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 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.

UR - http://www.scopus.com/inward/record.url?scp=46449103239&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=46449103239&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:46449103239

VL - 60

SP - 65

EP - 70

JO - Match

JF - Match

SN - 0340-6253

IS - 1

ER -