On the homological identities for a finite homogeneous graphs

An application of the Atiyah–Bott identity for an investigation of the spectral characteristics of a finite $(q+1)$-homogeneous factorgraph $Y=\Gamma\setminus X$ is given ($X$ is an infinite $(q+1)$-homogeneous tree, $\Gamma$ is a free group of the isometries acting on $X$). Bibliography: 9 titles.