In this paper exact values for the projective dimension of edge ideals associated to some star related graphs and product graphs G\ \square\ P_2, when G=\ C_n,\ K_n and upper bounds for the projective dimension when G=\ P_n,\ W_n, are obtained. We have proved that pd(C_{n+1}\ \square\ P_2)= 2\big(n-\left\lfloor \frac{n}{4}\right\rfloor\big), pd(K_n\ \square\ P_2)= 2n-2 and pd(P_{n+1}\ \square \ P_2)\le n+3+\left\lfloor \frac{n-3}{2}\right\rfloor, pd(W_n\ \square\ P_2)\leq n+1+\lceil\frac{2n-1}{3}\rceil. These values are functions of the number of vertices in the corresponding graphs.



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 Balakrishnan, Sneha,  Rosemary, Ruby, Thankachan, Reji