On extremal unicyclic molecular graphs with maximal Hosoya index
نویسندگان
چکیده
منابع مشابه
Some extremal unicyclic graphs with respect to Hosoya index and Merrifield-Simmons index
The Hosoya index of a graph is defined as the total number of the matchings, including the empty edge set, of the graph. The Merrifield-Simmons index of a graph is defined as the total number of the independent vertex sets, including the empty vertex set, of the graph. Let U(n,∆) be the set of connected unicyclic graphs of order n with maximum degree ∆. We consider the Hosoya indices and the Me...
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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 Un,d be the set of connected unicyclic (molecular) graphs of order n with diameter d. In this paper we completely characterize the graphs from Un,d minimizing the Hosoya index and determine the values of corresponding indices. Moreover, the third smallest Hos...
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Let T be an acyclic graph without perfect matching and Z(T ) be its Hosoya index; let Fn be the nth Fibonacci number. It is proved in this work that Z(T ) ≤ 2F2m F2m+1 when T has order 4m with the equality holding if and only if T = T1,2m−1,2m−1, and that Z(T ) ≤ F2 2m+2 + F2m F2m+1 when T has order 4m + 2 with the equality holding if and only if T = T1,2m+1,2m−1, where m is a positive integer ...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2009
ISSN: 0166-218X
DOI: 10.1016/j.dam.2008.06.006