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Divisor graph of set of all polynomials of degree at most two from Zp[x]

We denote by D(Zp[x, 2]), the divisor graph of set of all polynomials of degree at most two whose coefficients are from field Zp as its vertex set and any two distinct vertices in it are adjacent if one is a divisor of the other. In the present paper, we determine the degree of each vertex of the divisor graph D(Zp[x, 2]) and also study its characteristics as complete and/or cyclic or not. We also determine girth, size, degree sequence and irregularity index for the graph D(Zp[x, 2]). We also derive necessary and sufficient condition for D(Zp[x, 2]) to be Hamiltonian and/or Eulerian.