On automorphisms of 4-isoregular graphs

Graph $\Gamma$ is called t-isoregular, if for each $i\le t$ the number of common neighbours of $i$-vertex subgraph $\Delta$ depends only on the isomorphism type of $\Delta$. It is known that 4-isoregular graph is a regular complete multipartite graph, pentagon, $3\times3$-grid or pseudo-geometric graph for for $pG_r(2r,(2r-1)(r+1)^2)$ (or the complement of such a graph). In this paper it is obtained formulas for the character values of automorphisms of strongly regular subgraphs of pseudo-geometric graph $\Gamma$ for $pG_r(2r,(2r-1)(r+1)^2)$. It is investigated the case, when a subgraph of fixed points of automorphism of prime order of $\Gamma$ is empty, clique or coclique.