Journal of the Operations Research Society of China ›› 2019, Vol. 7 ›› Issue (4): 615-628.doi: 10.1007/s40305-018-0221-7

Special Issue: Discrete optimization

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Super-Edge-Connectivity and Zeroth-Order Randić Index

Zhi-Hong He1, Mei Lu2   

  1. 1 School of Mathematics and Information Science, Yantai University, Yantai 264005, Shandong, China;
    2 Department of Mathematical Science, Tsinghua University, Beijing 100084, China
  • Received:2017-08-27 Revised:2018-07-17 Online:2019-11-30 Published:2019-11-28
  • Contact: Zhi-Hong He, Mei Lu E-mail:zhihhe@126.com;mlu@math.tsinghua.edu.cn
  • Supported by:
    This work is supported by the National Natural Science Foundation of China (Nos. 11501490, 61373019, 13071107) and by the Natural Science Foundation of Shandong Province (No. ZR2015AM006).

Abstract: Define the zeroth-order Randić index R0(G)=∑xV(G) 1/√dG (x), where dG(x) denotes the degree of the vertex x. In this paper, we present two sufficient conditions for graphs and triangle-free graphs to be super-edge-connected in terms of the zeroth-order Randić index, respectively.

Key words: Zeroth-order Randić index, Super-edge-connected, Degree, Triangle-free graph, Minimum degree

CLC Number: