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In this paper, we found the Moore-Penrose generalized inverse of adjacencymatrix of an undirected graph, explicitly. We proved that the matrix$R_\lambda= [r_{ij}]$ is nonsingular where $r_{ii}=\frac{1}{\lambda}+ \deg v_i$and $r_{ij}=\mid N_G(V_i)\cap N_G(V_j)\mid$ for $i\neq j$, and we proved that$A^{\dagger}_G=[s_{ij}]_{1\leq i, j \leq n}$ where$\displaystyle{s_{ij}=s_{ji}=\lim_{\lambda \rightarrow +\infty} \langleR^{-1}_{\lambda}e_j, f_i \rangle }$. The proof of the main result was based onthe Tikhonov regularization.

Application of Tikhonov Regularization in Generalized Inverse of Adjacency Matrix of Undirected Graph