Sažetak By using the topological index Z and Z-counting polynomial proposed by the present author isospectral (IS) pairs of acyclic conjugated polyenes (C2nH2n+2) were studied. Besides the hitherto known smallest pair of n = 6, four and twenty seven pairs of n = 7 and 8, respectively, were first reported. Inspection of these results revealed several new features of IS tree graphs, i.e., appearance of two pairs of endospectral vertices in a tree graph and existence of several families of IS pair graphs whose Z-indices systematically grow up to infinity. Further several IS pairs were found to be closely related with each other topologically and called “intrinsic” IS pairs. Important role of the Z-index for analyzing the IS graphs is demonstrated.