We study the Ihara zeta function of the dumbbell graph $D_{1,1,n}$ of type (1, 1, n) and $D_{1,2,n}$ of type (1, 2, n). Explicit formulas of the zeta functions of the graphs, their radius of convergence, and the connection with the number of closed cy...
We study the Ihara zeta function of the dumbbell graph $D_{1,1,n}$ of type (1, 1, n) and $D_{1,2,n}$ of type (1, 2, n). Explicit formulas of the zeta functions of the graphs, their radius of convergence, and the connection with the number of closed cycles are given.