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 problem of how to estimate diffusion on a graph effectively is ofimportance both theoretically and practically. In this paper, we make use oftwo widely studied indices, geodesic distance and mean first-passage time($MFPT$) for random walk, to consider such a problem on some treelike models ofinterest. To this end, we first introduce several types of operations, forinstance, $m$th-order subdivision and ($1,m$)-star-fractal operation, togenerate the potential candidate models. And then, we develop a class of noveltechniques based on mapping for calculating the exact formulas of the bothquantities above on our models. Compared to those previous tools includingmatrix-based methods for addressing the issue of this type, the techniquesproposed here are more general mainly because we generalize the initialcondition for creating these models. Meantime, in order to show applications ofour techniques to many other treelike models, the two popularly discussedmodels, Cayley tree $C(t,n)$ and Exponential tree $\mathcal{T}(t;m)$, arechosen to serve as representatives. While their correspondence solutions havebeen reported, our techniques are more convenient to implement than thosepre-existing ones and thus this certifies our statements strongly. Final, wedistinguish the difference among results and attempt to make some heuristicexplanations to the reasons why the phenomena appear.

Determining Geodesic Distance on Arbitrary-order Subdivision of Tree with Applications