Design of crystal-like lattices can be achieved by using some net operations. Hypothetical networks, thus obtained, can be characterized in their topology by various counting polynomials and topological indices derived from them. The networks herein presented are related to the Dyck graph and described in terms of Omega polynomial and PIv polynomials.

Abstract In this paper the class of Brauer graph algebras is proved to be closed under derived equivalence. For that we use rank maximal torus identity component $$Out^0(A)$$ O u t 0 ( A )</mml:m...

A biologically motivated individual-based framework for evolution in network-structured populations is developed that can accommodate eco-evolutionary dynamics. This used to construct a network birth and death model. The evolutionary graph theory model, which considers dynamics only, derived as special case, highlighting additional assumptions diverge from real biological processes. achieved by...

In part I, we showed that there was an infinite family of graphs not embeddable in the torus in such a way that a free action of any group on any of the graphs extends to a cellular automorphism of the torus. We used a homologically-driven analysis of ordinary voltage graph embeddings. An ordinary voltage graph embedding with voltage group A in a surface encodes a derived embedding of a derived...

A graph polynomial q(G; ) has recently been studied byArratia et al. [The interlace polynomial: a new graph polynomial, in: Proceedings of the EleventhAnnual ACM-SIAM Symposium on Discrete Mathematics, San Francisco, CA, 2000, North-Holland, Amsterdam, pp. 237–245]. That polynomial can be derived from the restricted Tutte–Martin polynomial of an isotropic system, which we introduced [A. Bouchet...

. In this paper, we consider coding of short data frames (192 bits) by IRA codes. A new interleaver for the IRA codes based on a Gruenbaum graph is proposed. The difference of the proposed algorithm from known methods consists in the following: permutation is performed by using a match smaller interleaver which is derived from the Gruenbaum graph by finding in this graph a Hamiltonian path, enu...