Sufficient Conditions for a Graph to Be ℓ -Connected, ℓ -Deficient, ℓ -Hamiltonian and ℓ − -Independent in Terms of the Forgotten Topological Index

Guifu Su, Shuai Wang, Junfeng Du, Mingjing Gao, Kinkar Chandra Das and Yilun Shang
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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

Mathematics, 2022, vol. 10, issue 11, 1-11

Abstract: 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.

Keywords: the forgotten topological index; ? -connected; ? -deficient; ? -Hamiltonian; ? ? -independent (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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