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

The topic is the average order $A(G)$ of a connected induced subgraph of agraph $G$. This generalizes, to graphs in general, the average order of asubtree of a tree. In 1984, Jamison proved that the average order, over alltrees of order $n$, is minimized by the path $P_n$, the average being$A(P_n)=(n+2)/3$. In 2018, Kroeker, Mol, and Oellermann conjectured that $P_n$minimizes the average order over all connected graphs $G$ - a conjecture thatwas recently proved. In this short note we show that this lower bound can beimproved if the connectivity of $G$ is known. If $G$ is $k$-connected, then\[A(G) \geq \frac{n}2 \Bigg (1- \frac{1}{2^k+1} \Bigg ).\]

The Average Size of a Connected Vertex Set of a $k$-connected Graph