Recurrence relation on the number of spanning trees of generalized book graphs and related family of graphs

The book graph denoted by $B_{n,2}$ is the cartesian product $S_{n+1} times P_2$ where $S_{n+1}$ is a star graph with $n$ vertices of degree $1$ and one vertex of degree $n$ and $P_2$ is the path graph of $2$ vertices. Let $tau(B_{n,2})$ denote the number of spanning trees of $B_{n,2}$. Let $X_{n,p}$ denote the generalized form of book graph where a family of $p$-cycles which are $n$ in number is merged at a common edge. In this paper, we discuss some recurrence relations satisfied by $X_{n,p}$ and spanning trees of these associated family of graphs.