In this paper, for a simple undirected connected graph G, the concept of the distance Randić matrix of G is defined and basic properties on its spectrum are derived. Moreover, the distance Randić 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 Randić matrix of G is studied and bounds on its energy are obtained.

中文翻译：

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连通图的距离兰迪奇矩阵

在本文中，对于一个简单的无向连通图G，定义了G的距离Randić矩阵的概念，并推导了其频谱的基本性质。此外，引入了G的距离Randić能量。获得了该能量的界线，对于那些尖锐的，将描绘出极值图。最后，对于\（\ alpha \ in [0,1] \），研究了G的\（\ alpha-\）距离Randić矩阵的概念，并获得了其能量的界。