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

In the study of topological indices two negative correlations are well known:that between the number of subtrees and the Wiener index (sum of distances),and that between the Merrifield-Simmons index (number of independent vertexsubsets) and the Hosoya index (number of independent edge subsets). That is,among a certain class of graphs, the extremal graphs that maximize one indexusually minimize the other, and vice versa. In this paper, we first study thenumbers of subtrees in unicyclic graphs and unicyclic graphs with a givengirth, further confirming its opposite behavior to the Wiener index bycomparing with known results. We then consider the unicyclic graphs with agiven segment sequence and characterize the extremal structure with the maximumnumber of subtrees. Furthermore, we show that these graphs are not extremalwith respect to the Wiener index. We also identify the extremal structures thatmaximize the number of independent vertex subsets among unicyclic graphs with agiven segment sequence, and show that they are not extremal with respect to thenumber of independent edge subsets. These results may be the first exampleswhere the above negative correlation failed in the extremal structures betweenthese two pairs of indices.

Subtrees and independent subsets in unicyclic graphs and unicyclic graphs with fixed segment sequence