Vladimir Bozovic

We consider the group action of the automorphism group $\I_n=\aut(\Zz_n)$ on the set $\Zz_n$, that is the set of residue classes modulo $n$. Clearly, this group action provides a representation of $\I_n$ as a permutation group acting on $n$ points. One problem to be solved regarding this group action is to find its cycle index. Once it is found, there appears a vast class of related enumerative and computational problems with interesting applications. We provided the cycle index of specified group action in two ways. One of them is more abstract and hence compact, while another one is basically procedure of composing the cycle index from some \textit{building blocks}. However, those \textit{building blocks} are also well explained and finally presented in very detailed fashion.

We are looking for the graphs with minimal detour index in the class of connected bicyclic graphs. For the fixed number of vertices, we split the problem into two cases: bicyclic graphs without common edges between cycles and the complement of it. In both cases, we find graphs with minimal detour index.

A novel scheme for securing biometric templates of variable size and order is proposed. The proposed scheme is based on a new similarity measure approach, namely the set intersection, which strongly resembles the methodology used in most of the current state-of-the-art biometrics matching systems. The applicability of the new scheme is compared with that of the existing principal schemes, and it is shown that the new scheme has definite advantages over the existing approaches. The proposed scheme is analyzed both in terms of security and performance.