Estimations for the number of cycles in a graph (Q1375625)

The paper offers some bounds on \(\nu(G)\), the number of cycles in an undirected graph \(G\). The bounds are mainly lower bounds, and in terms of \(\delta\), the minimal degree of the graph \(G\). For a loopless graph \(G\) we have \(\nu(G) \geq 1/2 \delta(\delta-1)\). If \(|V(G)|\geq 3\) and \(\delta \geq 5\) then \(\nu(G) \geq \delta(\delta-1)\), etc. There are even better bounds for special graphs, such as Hamiltonian or block graphs.