On investigations of graphs preserving the Wiener index upon vertex removal

AIMS Mathematics

Zijiang Zhu¹  Yi Hu¹  Pu Wu²  Zehui Shao²  Asfand Fahad³ 

[1] 1. School of Information Science and Technology, South China Business College of Guangdong University of Foreign Studies, 510545, Guangzhou, China 2. Institute for Intelligent Information Processing, South China Business College of Guangdong University of Foreign Studies, 510545, Guangzhou, China;3. Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China;4. Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari 61100, Pakistan;

关键词: wiener index;    vertex removal;    topological index;   

DOI  :  10.3934/math.2021750

来源: DOAJ

【 摘 要 】

In this paper, we present solutions of two open problems regarding the Wiener index $ W(G) $ of a graph $ G $. More precisely, we prove that for any $ r \geq 2 $, there exist infinitely many graphs $ G $ such that $ W(G) = W(G - \{v_1, \ldots, v_r\}) $, where $ v_1, \ldots, v_r $ are $ r $ distinct vertices of $ G $. We also prove that for any $ r \geq 1 $ there exist infinitely many graphs $ G $ such that $ W(G) = W(G - \{v_i\}) $, $ 1 \leq i \leq r $, where $ v_1, \ldots, v_r $ are $ r $ distinct vertices of $ G $.

【 授权许可】

Unknown