English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Degree sequence (DS) problems are around for at least hundred twenty years,and with the advent of network science, more and more complicated, structuredDS problems were invented. Interestingly enough all those problems so far arecomputationally easy. It is clear, however, that we will find sooncomputationally hard DS problems. In this paper we want to find such hard DSproblems with relatively simple definition.  For a vertex $v$ in the simple graph $G$ denote $d_i(v)$ the number ofvertices at distance exactly $i$ from $v$. Then $d_1(v)$ is the usual degree ofvertex $v.$ The vector $\mathbf{d}^2(G)=( (d_1(v_1), d_2(v_1)), \ldots,$$(d_1(v_n), d_2(v_n))$ is the {\bf second order degree sequence} of the graph$G$. In this note we show that the problem to decide whether a sequence ofnatural numbers $((i_1,j_1),\ldots (i_n,j_n))$ is a second order degreesequence of a simple undirected graph $G$ is strongly NP-complete. Then we willdiscuss some further NP-complete DS problems.

Not all simple looking degree sequence problems are easy