Journals Information
Mathematics and Statistics Vol. 13(1), pp. 62 - 67
DOI: 10.13189/ms.2025.130108
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Parity Weighted Totally Antimagic Total Graphs
G. Suthakaran , R. Jeyabalan *
Department of Mathematics, Alagappa University, Karaikudi, India
ABSTRACT
This manuscript presents a new development in graph labeling by exploring parity-weighted totally antimagic total (TAT) labeling. A parity-weighted TAT labeling is a TAT labeling in which all vertex and edge weights are either even or odd. If all vertex weights are even (or odd) and all edge weights are odd (or even), the labeling can be defined as strong (SPAT) or weak (WPAT) parity-weighted TAT labeling, respectively. The primary objective of this study is to determine whether specific graph families- namely, friendship graphs, generalized friendship graphs, fan graphs, and wheel graphs- admit SPAT or WPAT labeling. Key findings of the research identify conditions under which SPAT and WPAT labeling are possible, demonstrating the uniqueness of certain graph families in admitting these schemes. The results provide a foundation for further exploration of parity-constrained labeling in graph theory. The primary aim is not just to characterize these graphs and extend the theoretical understanding of antimagic total labeling under parity constraints. The work addresses the problem of characterizing and understanding parity-constrained antimagic total labeling schemes, which are not well-explored in existing literature. This includes identifying graph families that admit these schemes and understanding their structural and theoretical implications. Constructive labeling techniques is employed to establish the existence of these labelings.
KEYWORDS
Antimagic, Totally Antimagic Total Graphs, Perfectly Antimagic Total Graphs, Friendship Graph
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] G. Suthakaran , R. Jeyabalan , "Parity Weighted Totally Antimagic Total Graphs," Mathematics and Statistics, Vol. 13, No. 1, pp. 62 - 67, 2025. DOI: 10.13189/ms.2025.130108.
(b). APA Format:
G. Suthakaran , R. Jeyabalan (2025). Parity Weighted Totally Antimagic Total Graphs. Mathematics and Statistics, 13(1), 62 - 67. DOI: 10.13189/ms.2025.130108.