On extremal unicyclic molecular graphs with maximal Hosoya index |
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Authors: | Jianping Ou |
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Affiliation: | Department of Mathematics & Physics, Wuyi University, Jiangmen 529020, China |
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Abstract: | Let G be a unicyclic n-vertex graph and Z(G) be its Hosoya index, let Fn stand for the nth Fibonacci number. It is proved in this paper that Z(G)≤Fn+1+Fn−1 with the equality holding if and only if G is isomorphic to Cn, the n-vertex cycle, and that if G≠Cn then Z(G)≤Fn+1+2Fn−3 with the equality holding if and only if G=Qn or Dn, where graph Qn is obtained by pasting one endpoint of a 3-vertex path to a vertex of Cn−2 and Dn is obtained by pasting one endpoint of an (n−3)-vertex path to a vertex of C4. |
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Keywords: | Hosoya index Unicyclic molecular graph Matching |
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