Reciprocal degree distance and Hamiltonian properties of graphs

Abstract

For a connected graph G, the reciprocal degree distance (RDD) of the graph G is defined as; RDD(G)=∑u≠vdegG⁡(u)+degG⁡(v)dG(u,v), where degG⁡(u) is the degree of u in G and dG(u,v) is the distance between u and v in G. In this article, we give sufficient condition for a graph to be traceable, Hamiltonian, Hamiltonian-connected in terms of RDD(G).