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, Yilun Shang
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.
Topics & Concepts
Topological indexMathematicsVertex (graph theory)Topological graph theoryGraphGraph propertyTopology (electrical circuits)Voltage graphCombinatoricsTopological graphHamiltonian (control theory)Line graphDiscrete mathematicsMathematical optimizationGraph theory and applicationsTopological and Geometric Data AnalysisComputational Drug Discovery Methods