A proper total coloring distinguishing adjacent vertices by sums of some product graphs
Add this Pith Number to your LaTeX paper
What is a Pith Number?\usepackage{pith}
\pithnumber{7VTZDQ67}
Prints a linked pith:7VTZDQ67 badge after your title and writes the identifier into PDF metadata. Compiles on arXiv with no extra files. Learn more
read the original abstract
In this article, we consider a proper total coloring distinguishes adjacent vertices by sums, if every two adjacent vertices have different total sum of colors of the edges incident to the vertex and the color of the vertex. Pilsniak and Wozniak \cite{PW} first introduced this coloring and made a conjecture that the minimal number of colors need to have a proper total coloring distinguishes adjacent vertices by sums is less than or equal to the maximum degree plus $3$. We study proper total colorings distinguishing adjacent vertices by sums of some graphs and their products. We find that these graphs satisfy the conjecture.
This paper has not been read by Pith yet.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.