Energy, Hosoya index and Merrifield–Simmons index of trees with prescribed degree sequence
نویسندگان
چکیده
منابع مشابه
Chemical 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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We characterize the trees T with n vertices whose Hosoya index (total number of matchings) is Z(T ) > 16fn−5 resp. the trees whose Merrifield-Simmons index (total number of independent subsets) is σ(T ) < 18fn−5 + 21fn−6, where fk is the kth Fibonacci number. It turns out that all the trees satisfying the inequality are tripodes (trees with exactly three leaves) and the path in both cases. Furt...
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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 a rooted tree and ni(t) the number of nodes in t having i children. The degree sequence (ni(t), i ≥ 0) of t satisfies ∑ i≥0 ni(t) = 1 + ∑ i≥0 ini(t) = |t|, where |t| denotes the number of nodes in t. In this paper, we consider trees sampled uniformly among all plane trees having the same degree sequence s; we write Ps for the corresponding distribution. Let s(κ) = (ni(κ), i ≥ 0) be a l...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2013
ISSN: 0166-218X
DOI: 10.1016/j.dam.2012.10.010