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Maximum zeroth-order general Randić index of orientations of cacti · arXivDesk

2205.09955May 20, 2022zeroth-order general Randić index; cactus; extremal graph

Maximum zeroth-order general Randić index of orientations of cacti

Jiaxiang Yang, Hanyuan Deng, Zikai Tang, Hechao Liu

General Mathematics

Abstract

The zeroth-order general Randić index $R^{0}_{a+1}$ of an $n$ -vertices oriented graph $D$ is equal to the sum of $(d^{+}_{u_i})^{a}+(d^{-}_{u_j})^{a}$

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Nearby in the stack

over all arcs

u_iu_j

of

D

, where we denote by

d^{+}_{u_i}

the out-degree of the vertex

u_i

and

d^{-}_{u_j}

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\geq 1

.

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