Totally antimagic total labeling of ladders, prisms and generalised Petersen graphs

Akwu, Abolape Deborah; Ajayi, Deborah Olayide A.

doi:10.47974/JDMSC-1229

Open Access Research Article

Totally antimagic total labeling of ladders, prisms and generalised Petersen graphs

^*Abolape Deborah AkwuCorresponding authorabolaopeyemi@yahoo.co.ukDepartment of Mathematics Federal University of AgricultureMakurdi, NigeriaView full profile → , Deborah Olayide A. Ajayiadelaideajayi@yahoo.com and olayide.ajayi@ui.edu.ngDepartment of Mathematics University of IbadanIbadan, NigeriaView full profile →

* Corresponding author · click or hover a name for details

pp. 31–44Vol. 27Issue 1January 2024DOI: 10.47974/JDMSC-1229 Crossmark XML

Received:: 05 May 2020
Accepted:: 15 Sep 2020
Published Online:: 24 Jan 2024
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1229
Pages:: 31–44

Abstract

A total labeling is called edge-antimagic total (vertex-antimagic total) if all edge-weights (vertex-weights) are pairwise distinct. If a labeling is simultaneously edge-antimagic total and vertex-antimagic total, it is called a totally antimagic total labeling. A graph that admits totally antimagic total labeling is called a totally antimagic total graph. In this paper, we prove that ladders, prisms and generalised Pertersen graphs are totally antimagic total graphs. We also show that the chain graph of totally antimagic total graphs is a totally antimagic total graphs.

Keywords

Graph labeling Ladders Chain graphs Prisms and generalised petersen graph

Subject Classifications

(2010) 05C78

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