Document Type : Original Article

**Authors**

Department of mathematics, statistics and computer science of Semnan university

**Abstract**

Given a graph G with vertex set V (G) = {v1, v2, · · · , vn}. Let di be the degree of the vertex vi in G for i = 1,2, · · ·, n. We introduce the sum of degrees and the product of degrees matrices of a graph. Furthermore, we consider the central indices matrix as an Arithmetic mean matrix, Geometric mean matrix, and Harmonic mean matrix. The spectral of these matrices has been computed. In this paper, we investigate the central indices energy of some classes of graphs and several results concerning its energy have been obtained.

**Graphical Abstract**

**Keywords**

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July 2023

Pages 105-112

**Receive Date:**27 May 2023**Revise Date:**07 June 2023**Accept Date:**22 June 2023**Publish Date:**01 July 2023