Sharp bounds on the zeroth-order general Randić index of trees in terms of domination number

2021/03/29 by Chang Liu, Jianping Li, Liu, Chang +1
Chemistry · Computer Science · Mathematics · #05C35 #05C50 #05C69 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Interconnection Networks and Systems #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.2103.15288

openalex publication_date 2021/03/29 · openalex created_date 2021/04/13 · openalex updated_date 2026/07/28

Abstract

The zeroth-order general Randić index of graph G=(V_G,E_G), denoted by ⁰R_α(G), is the sum of items (d_v)^α over all vertices v∈ V_G, where α is a pertinently chosen real number. In this paper, we obtain the sharp upper and lower bounds on ⁰R_α of trees with a domination number γ, in intervals α∈(-∞,0)∪(1,∞) and α∈(0,1), respectively. The corresponding extremal graphs of these bounds are also characterized.

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