Abstract
In this paper we mainly prove that let G be a (k + 1)-edge-connected simple graph of order n with girth g. Then G is upper embeddable if \( \sum\limits_{v \in I(G)} {d_G (v) \geqslant n - 2g + 5 - 3k - (g - 5)k^2 } \) for any independent set I(G) = {υi | 1 ⩽ i ⩽ k2 + 2}, k = 0,1,2 and the lower bound is tight.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.