Given a connected graph H, its reciprocal degree distance is defined as where denotes the degree of the vertex in the graph H and is the shortest distance between and 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.
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