Open Journal of Discrete Applied Mathematics
Vol. 6 (2023), Issue 3, pp. 22 – 25
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2023.0089
On the super edge-magicness of graphs with a specific degree sequence
Rikio Ichishima\(^{1,*}\), Francesc-Antoni Muntaner-Batle\(^{2}\)
\(^{1}\)Department of Sport and Physical Education, Faculty of Physical Education, Kokushikan University, 7-3-1 Nagayama, Tama-shi, Tokyo 206-8515, Japan.; ichishim@kokushikan.ac.jp
\(^{2}\)Graph Theory and Applications Research Group, School of Electrical Engineering and Computer Science, Faculty of Engineering and Built Environment, The University of Newcastle, NSW 2308 Australia.; famb1es@yahoo.es
Copyright © 2023 Rikio Ichishima and Francesc-Antoni Muntaner-Batle. 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: August 14, 2023 – Accepted: September 26, 2023 – Published: December 26, 2023
Abstract
A graph \(G\) is said to be super edge-magic if there exists a bijective function \(f:V\left(G\right) \cup E\left(G\right)\rightarrow \left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert +\left\vert E\left( G\right) \right\vert \right\}\) such that \(f\left(V \left(G\right)\right) =\left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert \right\}\) and \(f\left(u\right) + f\left(v\right) + f\left(uv\right)\) is a constant for each \(uv\in E\left( G\right)\). In this paper, we study the super edge-magicness of graphs of order \(n\) with degree sequence \(s:4, 2, 2, \ldots, 2\). We also investigate the super edge-magic properties of certain families of graphs. This leads us to propose some open problems.
Keywords:
(Super) edge-magic graph; (Super) edge-magic labeling; Vertex degree; Degree sequence; Graph labeling.