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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this article, we consider a proper total coloring distinguishes adjacentvertices by sums, if every two adjacent vertices have different total sum ofcolors of the edges incident to the vertex and the color of the vertex.Pilsniak and Wozniak \cite{PW} first introduced this coloring and made aconjecture that the minimal number of colors need to have a proper totalcoloring distinguishes adjacent vertices by sums is less than or equal to themaximum degree plus $3$. We study proper total colorings distinguishingadjacent vertices by sums of some graphs and their products. We find that thesegraphs satisfy the conjecture.

A proper total coloring distinguishing adjacent vertices by sums of some product graphs