Minimizing a class of unicyclic graphs by means of Hosoya index
نویسندگان
چکیده
منابع مشابه
The smallest Hosoya index of unicyclic graphs with given diameter∗
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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The detour index of a connected graph is defined as the sum of detour distances between all unordered pairs of vertices. We determine the n-vertex unicyclic graphs whose vertices on its unique cycle all have degree at least three with the first, the second and the third smallest and largest detour indices respectively for n ≥ 7.
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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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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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The Harmonic index $ H(G) $ of a graph $ G $ is defined as the sum of the weights $ dfrac{2}{d(u)+d(v)} $ of all edges $ uv $ of $G$, where $d(u)$ denotes the degree of the vertex $u$ in $G$. In this work, we prove the conjecture $dfrac{H(G)}{D(G)} geq dfrac{1}{2}+dfrac{1}{3(n-1)} $ given by Jianxi Liu in 2013 when G is a unicyclic graph and give a better bound $ dfrac{H(G)}{D(G)}geq dfra...
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ژورنال
عنوان ژورنال: Mathematical and Computer Modelling
سال: 2008
ISSN: 0895-7177
DOI: 10.1016/j.mcm.2007.12.003