Minimizing a class of unicyclic graphs by means of Hosoya index

Authors:
Hongbo Hua
Affiliations:
Department of Computing Science, Huaiyin Institute of Technology, Huaian, Jiangsu 223000, PR China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2008

Citing 2
Cited 2

On acyclic systems with minimal Hosoya index

Discrete Applied Mathematics
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Graph Theory With Applications

Maxima and Minima of the Hosoya Index and the Merrifield-Simmons Index

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On the number of independent subsets in trees with restricted degrees

Mathematical and Computer Modelling: An International Journal

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Abstract

The Hosoya index, denoted by z(G), of a (molecular) graph G is defined as the total number of independent-edge sets of G. Let U"n be the set of unicyclic graphs with n vertices. A fully loaded unicyclic graph is a unicyclic graph with the property that there is no vertex with degree less than 3 in its unique cycle. Denote by U"n^1 the set of fully loaded unicyclic graphs. In this paper, graphs in U"n^1 with minimal, second-minimal and third-minimal Hosoya indices are uniquely determined, respectively.