Open Journal of Discrete Applied Mathematics
Vol. 7 (2024), Issue 2, pp. 7 – 10
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2024.0098
The inverse degree conditions for Hamiltonian and traceable graphs
Rao Li\(^{1,*}\)
\(^{1}\)Dept. of Computer Science, Engineering, and Math University of South Carolina Aiken, Aiken, SC 29801; raol@usca.edu
Copyright © 2024 Rao Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: May 10, 2024 – Accepted: June 09, 2024 – Published: June 30, 2024
Abstract
Let \(G = (V(G), E(G))\) be a graph with minimum degree at least \(1\). The inverse degree of \(G\), denoted \(Id(G)\), is defined as the sum of the reciprocals of degrees of all vertices in \(G\). In this note, we present inverse degree conditions for Hamiltonian and traceable graphs.
Keywords:
the inverse degree; Hamiltonian graph, traceable graph.