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

We generalize two main theorems of matching polynomials of undirected simplegraphs, namely, real-rootedness and the Heilmann-Lieb root bound. Viewing thematching polynomial of a graph $G$ as the independence polynomial of the linegraph of $G$, we determine conditions for the extension of these theorems tothe independence polynomial of any graph. In particular, we show that astability-like property of the multivariate independence polynomialcharacterizes claw-freeness. Finally, we give and extend multivariate versionsof Godsil's theorems on the divisibility of matching polynomials of treesrelated to $G$.

Generalizations of the Matching Polynomial to the Multivariate Independence Polynomial