2010/04/11 by Xueliang Li, Yiyang Li, Li, Xueliang +1
Chemistry · Mathematics · #05A15 #05A16 #05C05 #05C12 #05C30 #05D40 #92E10 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph theory and applications #Molecular spectroscopy and chirality #Synthesis and Properties of Aromatic Compounds
paper · pdf · doi:10.48550/arxiv.1004.1778
openalex publication_date 2010/04/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Let \mathcal TΔn denote the set of trees of order n, in which the degree of each vertex is bounded by some integer Δ. Suppose that every tree in \mathcal TΔn is equally likely. We show that the number of vertices of degree j in \mathcal TΔn is asymptotically normal with mean (μj+o(1))n and variance (σj+o(1))n, where μj, σj are some constants. As a consequence, we give estimate to the value of the general Zagreb index for almost all trees in \mathcal TΔn. Moreover, we obtain that the number of edges of type (i,j) in \mathcal TΔn also has mean (μij+o(1))n and variance (σij+o(1))n, where an edge of type (i,j) means that the edge has one end of degree i and the other of degree j, and μij, σij are some constants. Then, we give estimate to the value of the general Randić index for almost all trees in \mathcal TΔn.