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Bounds of the general Randi\'{c} Estrada index of a graph

GAO Nan1,2,*  LI Meili2  SHE Yanhong2   

  1. 1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China 2. College of Science, Xi'an Shiyou University, Xi'an 710065, China
  • Received:2016-05-23 Online:2017-09-15 Published:2017-09-15

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Abstract:

Motivated by the Randi\'{c} Estrada index and the general Randi\'{c} energy of a graph, we define the concept of general Randi\'{c} Estrada index of a graph. By using the algebraic and elementary analysis method, we obtain lower and upper bounds for the general Randi\'{c} Estrada index of a simple connected graph of order n and an r-regular graph, which generalize the results of Bozkurt et. al. on the Randi\'{c} Estrada of a graph.

Key words: Randi\'{c} Estrada index, general Randi\'{c} energy, general Randi\'{c} Estrada index