Maximum zeroth-order general Randić index of orientations of cacti

2022/05/20 by Jiaxiang Yang, Hanyuan Deng, Yang, Jiaxiang +5
Mathematics · Computer Science · #Graph theory and applications #Graph Labeling and Dimension Problems #Advanced Graph Theory Research

paper · pdf · doi:10.48550/arxiv.2205.09955

Abstract

The zeroth-order general Randić index R⁰_a+1 of an n-vertices oriented graph D is equal to the sum of (d⁺_ui)^a+(d^-_uj)^a over all arcs u_iu_j of D, where we denote by d⁺_ui the out-degree of the vertex u_i and d^-_uj the in-degree of the vertex u_j, a is an arbitrary real number. In the paper, we determine the orientations of cacti with the maximum value of the zeroth-order general Randić index for a≥ 1.

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