Open Journal of Discrete Applied Mathematics
Vol. 7 (2024), Issue 2, pp. 1 – 6
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2024.0097
Note: Certain bounds in respect of upper deg-centric graphs
Johan Kok\(^{1,*}\)
\(^{1}\)Independent Mathematics Researcher, City of Tshwane, South Africa & Visiting Faculty at CHRIST (Deemed to be a University), Bangalore, India; jacotype@gmail.com; johan.kok@christuniversity.in
Copyright © 2024 Johan Kok. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: March 8, 2023 – Accepted: January 01, 2024 – Published: May 31, 2024
Abstract
This note presents some upper bounds for the size of the upper deg-centric grapg \(G_{ud}\) of a simple connected graph G. Amongst others, a result for graphs for which a compliant graph \(G\) has \(G_{ud} \cong \overline G\) is presented. Finally, results for size minimality in respect upper deg-centrication and minimum size of such graph \(G\) are presented.
Keywords:
Upper deg-centric graph; upper deg-centrication; equi-eccentric graph.