The Distance Randić Matrix of Connected Graphs

In this paper, for a simple undirected connected graph G, the concept of the distance Randic matrix of G is defined and basic properties on its spectrum are derived. Moreover, the distance Randic energy of G is introduced. Bounds on this energy are obtained and for those which are sharp the extremal graphs are characterized. Finally, for $$\alpha \in [0,1]$$ , the concept of $$\alpha -$$ distance Randic matrix of G is studied and bounds on its energy are obtained.