Sufficient Conditions for a Graph to Be <i>ℓ</i>-Connected, <i>ℓ</i>-Deficient, <i>ℓ</i>-Hamiltonian and <i>ℓ</i><sup>−</sup>-Independent in Terms of the Forgotten Topological Index
Guifu Su,
Shuai Wang,
Junfeng Du,
Mingjing Gao,
Kinkar Chandra Das,
Yilun Shang
Affiliations
Guifu Su
College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China
Shuai Wang
College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China
Junfeng Du
College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China
Mingjing Gao
College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China
Kinkar Chandra Das
Department of Mathematics, Sungkyunkwan University, Suwon 16419, Korea
Yilun Shang
Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK
The forgotten topological index of a (molecule) graph is the sum of cubes of all its vertex degrees, which plays a significant role in measuring the branching of the carbon atom skeleton. It is meaningful and difficult to explore sufficient conditions for a given graph keeping certain properties in graph theory. In this paper, we mainly explore sufficient conditions in terms of the forgotten topological index for a graph to be ℓ-connected, ℓ-deficient, ℓ-Hamiltonian and ℓ−-independent, respectively. The conditions cannot be dropped.
