The First Zagreb Index and Some Hamiltonian Properties of Graphs

Rao Li ()
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Rao Li: Department of Computer Science, Engineering and Mathematics, University of South Carolina Aiken, Aiken, SC 29801, USA

Mathematics, 2024, vol. 12, issue 24, 1-12

Abstract: Let G = ( V , E ) be a graph. The first Zagreb index of a graph G is defined as ∑ u ∈ V d G 2 ( u ) , where d G ( u ) is the degree of vertex u in G . A graph G is called Hamiltonian (resp. traceable) if G has a cycle (resp. path) containing all the vertices of G . Using two established inequalities, in this paper, we present sufficient conditions involving the first Zagreb index for Hamiltonian graphs and traceable graphs. We also present upper bounds for the first Zagreb index of a graph and characterize the graphs achieving the upper bounds.

Keywords: the first Zagreb index; Hamiltonian graph, traceable graph; upper bound (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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