The inverse degree conditions for Hamiltonian and traceable graphs

Author(s): Rao Li1
1Dept. of Computer Science, Engineering, and Math University of South Carolina Aiken, Aiken, SC 29801
Copyright © 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.

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.