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The power graph P(G) of a group G is the graph with group elements as vertex set and two elements are adjacent if one is a power of the other. The aim of this paper is to compute the automorphism group of the power graph of several well-known and important classes of finite groups.

For a simple graph G on n vertices, the signless Laplacian Estrada index is defined as SLEE(G) = n i=1 e q i , where q 1 , q 2 , . . . , q n are the eigenvalues of the signless Laplacian matrix of G. In this paper, the unique graph on n vertices with maximum signless Laplacian Estrada index is determined among graphs with given number of cut edges, pendent vertices, (vertex) connectivity and edge connectivity, respectively.

Given the many benefits that cloud computing brings, organizations tend to outsource most of their data to reduce a large portion of their costs, but concern about the privacy of data is a major obstacle to outsourcing sensitive data. To solve this problem, public key encryption with keyword search (PEKS) is suggested, which is a widely used method. Addressing this issue separately is beneficial because PEKS does not require a secure communication channel and key distribution. Therefore, at first glance, it seems that PEKS schemes should be used more in practical applications. Thus, reviewing and categorizing PEKS schemes are very important and necessary. In this article, we have tried to help reviewing the public key searchable encryption and categorizing these designs.