Original scientific paper

The smallest Hosoya index of unicyclic graphs with given diameter

Kexiang Xu ; College of Science, Nanjing University of Aeronautics $\&$ Astronautics, Nanjing, P. R. China

Abstract

The Hosoya index of a (molecular) graph is defined as the total number of the matchings, including the empty edge set,
of this graph. Let ${\cal{U}}_{n,d}$ be the set of connected unicyclic (molecular) graphs of order n with diameter d. In this paper we completely characterize the graphs from ${\cal{U}}_{n,d}$ minimizing the Hosoya index and determine the values of corresponding indices.
Moreover, the third smallest Hosoya index of unicyclic graphs is determined.

Keywords

osoya index; unicyclic (molecular) graph; diameter

Hrčak ID:

83077

URI

https://hrcak.srce.hr/83077

Publication date:

12.6.2012.

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