Some results on the 3‐total‐rainbow index

作者：

Highlights：

• Determine the 3-total-rainbow index of Cn.

• Investigate the 3-total-rainbow index of unicyclic graphs.

• Provide a sharp upper bound for the 3-total-rainbow index of general graphs.

• Determine the 3-total-rainbow index of all small cubic graphs of order 8 or less.

摘要

•Determine the 3-total-rainbow index of Cn.•Investigate the 3-total-rainbow index of unicyclic graphs.•Provide a sharp upper bound for the 3-total-rainbow index of general graphs.•Determine the 3-total-rainbow index of all small cubic graphs of order 8 or less.

论文关键词：Total-coloring,TRT-connecting,3-total-rainbow coloring,3-total-rainbow index,Total-rainbow 3-tree connected

论文评审过程：Received 17 February 2022, Revised 24 March 2022, Accepted 26 March 2022, Available online 22 April 2022, Version of Record 22 April 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127128