Zeta functions of several corona-type graphs

Ihara Zeta Function and Spectrum of the Cone Over a Semiregular Bipartite Graph

“…The following three lemmas [11,12,17] on matrix techniques will be used. Let M 11 , M 12 , M 21 and M 22 be n 1 × n 1 , n 1 × n 2 , n 2 × n 1 and n 2 × n 2 matrices, respectively.…”

“…Blanchard et al [3] studied the zeta function of the r-join of two regular graphs, and proved that their zeta functions are the same if and only if they have the same adjacency spectrum. Recently, Chen and Chen [5] studied Bartholdi zeta functions of the generalized join of some regular graphs along a fixed graph, Li and Hou [10] studied the zeta function of the cone of a semi-regular bipartite graph and Li et al [11] studied zeta functions of three types of corona graphs.…”