Lexicographic ordering by spectral moments ($S$-order) among all trees is discussed in this‎ ‎paper‎. ‎For two given positive integers $p$ and $q$ with $pleqslant q$‎, ‎we denote $mathscr{T}_n^{p‎, ‎q}={T‎: ‎T$ is a tree of order $n$ with a $(p‎, ‎q)$-bipartition}‎. Furthermore, ‎the last four trees‎, ‎in the $S$-order‎, ‎among $mathscr{T}_n^{p‎, ‎q},(4leqslant pleqslant q)$ are characterized‎.

This brief proposes a new algorithm to synthesize low power bipartition-codec architecture for pipelined circuits. The bipartition-codec architecture has been introduced as an effective power reduction technique for circuit design. The entropy-based partition-codec (ENPCO) algorithm extends this approach as it optimizes for both: power and area. It uses entropy as a criterion to balance between...

Topologically-ordered phases of matter at nonzero temperature are conjectured to exhibit universal patterns long-range entanglement, which can be detected using the entanglement negativity, a mixed-state measure. In this paper, we show that negativity in certain topological orders understood through properties an emergent symmetry-protected (SPT) order is localized on bipartition. This connecti...

In this paper, we propose a bipartition dual-encoding architecture for low power pipelined circuit. Pipelined circuits consist of combinational logic blocks separated by registers which usually consume a large amount of power. Although the clock gated technique is a promising approach to reduce switching activities of the pipelined registers, this approach is restricted by the placement of the ...

For given a pair of nodes in a graph, the minimum non-separating path problem looks for a minimum weight path between the two nodes such that the remaining graph after removing the path is still connected. The balanced connected bipartition (BCP2) problem looks for a way to bipartition a graph into two connected subgraphs with their weights as equal as possible. In this paper we present an algo...

This paper introduces a trivariate graph polynomial that is a common generalization of the domination polynomial, the Ising polynomial, the matching polynomial, and the cut polynomial of a graph. This new graph polynomial, called the bipartition polynomial, permits a variety of interesting Research supported by ESF. Research supported by the Austrian National Research Network S11403-N23 (RiSE) ...

We calculate the bipartite Rényi entanglement entropy of an L× L× 2 bilayer Hubbard model using a determinantal quantum Monte Carlo method recently proposed by Grover [Phys. Rev. Lett. 111, 130402 (2013)]. Two types of bipartition are studied: (i) one that divides the lattice into two L× L planes and (ii) one that divides the lattice into two equal-size (L× L/2 × 2) bilayers. We compare our cal...

We present a new approach to analysing finite graphs which admit a vertex intransitive group of automorphisms G and are either locally (G, s)– arc transitive for s ≥ 2 or G–locally primitive. Such graphs are bipartite with the two parts of the bipartition being the orbits of G. Given a normal subgroup N which is intransitive on both parts of the bipartition, we show that taking quotients with r...