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An equiangular tight frame (ETF) is a d × n matrix that has orthogonal rows and unit-norm columns. ETFs have applications in communications, coding theory and quantum computing. In this paper we investigate type of ETFs that have n + 1 vectors in R n . Also we state the connection between these frames with the complete graphs that containing n + 1 vertices.doi:10.14419/ijamr.v1i4.309 fatcat:zgc4lx6w6jea3e5hbxmj4kn4l4