On acyclic systems with minimal Hosoya index
نویسندگان
چکیده
منابع مشابه
On acyclic systems with minimal Hosoya index
The Hosoya index of a graph is de*ned as the total number of independent edge subsets of the graph. In this note, we characterize the trees with a given size of matching and having minimal and second minimal Hosoya index. ? 2002 Elsevier Science B.V. All rights reserved.
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For a graph G, the Hosoya index and the Merrifield-Simmons index are defined as the total number of its matchings and the total number of its independent sets, respectively. In this paper, we characterize the structure of those graphs that minimize the Merrifield-Simmons index and those that maximize the Hosoya index in two classes of simple connected graphs with n vertices: graphs with fixed m...
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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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For a graph G, the Merrifield-Simmons index i(G) and the Hosoya index z(G) are defined as the total number of independent sets and the total number of matchings of the graph G, respectively. In this paper, we characterize the graphs with the maximal Merrifield-Simmons index and the minimal Hosoya index, respectively, among the bicyclic graphs on n vertices with a given girth g.
متن کاملChemical Trees Minimizing Energy and Hosoya Index
Abstract. The energy of a molecular graph is a popular parameter that is defined as the sum of the absolute values of a graph’s eigenvalues. It is well known that the energy is related to the matching polynomial and thus also to the Hosoya index via a certain Coulson integral. Trees minimizing the energy under various additional conditions have been determined in the past, e.g., trees with a gi...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2002
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(01)00306-7