In 1994, J. Chen, J. Gross, and R. Rieper demonstrated how to use the rank of Mohar's overlap matrix to calculate the crosscap‐number distribution, that is, the distribution of the embeddings of a graph in the nonorientable surfaces. That has ever since been by far the most frequent way that these distributions have been calculated. This article introduces a way to calculate the Euler‐genus polynomial of a graph, which combines the orientable and the nonorientable embeddings, without using the overlap matrix. The crosscap‐number polynomial for the nonorientable embeddings is then easily calculated from the Euler‐genus polynomial and the genus polynomial.
Journal of Graph Theory – Wiley
Published: Jan 1, 2018
Keywords: ; ; ; ; ; ;
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera