On reciprocal degree distance of graphs

Heliyon. 2023 Jul 4;9(7):e17914. doi: 10.1016/j.heliyon.2023.e17914. eCollection 2023 Jul.

Abstract

Given a connected graph H, its reciprocal degree distance is defined asRDD(H)=xydH(vx)+dH(vy)dH(vx,vy), where dH(vx) denotes the degree of the vertex vx in the graph H and dH(vx,vy) is the shortest distance between vx and vy in H. The goal of this paper is to establish some sufficient conditions to judge that a graph to be ħ-hamiltonian, ħ-path-coverable or ħ-edge-hamiltonian by employing the reciprocal degree distance.

Keywords: 05C09; 05C92; Reciprocal degree distance; ħ-edge-hamiltonian; ħ-hamiltonian; ħ-path-coverable.