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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Among all trees on $n$ vertices with a given degree sequence, how do wemaximise or minimise the sum over all adjacent pairs of vertices $x$ and $y$ of$f(\mathrm{deg} x, \mathrm{deg} y)$? Here $f$ is a fixed symmetric functionsatisfying a 'monotonicity' condition that \[  f(x, a) + f(y, b) > f(y, a) + f(x, b) \quad \mbox{for any $x > y$ and $a >b$} . \] These functions arise naturally in several areas of graph theory,particularly chemical graph theory.  Wang showed that the so-called 'greedy' tree maximises this quantity, whilean 'alternating greedy' tree minimises it. Our aim in this paper is to solvethe inverse problem: we characterise precisely which trees are extremal forthese two problems.

An inverse result for Wang's theorem on extremal trees