Mathematics and Statistics Vol. 12(3), pp. 234 - 239
DOI: 10.13189/ms.2024.120303
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Sharp Bounds on Vertex N-magic Total Labeling Graphs

R. Nishanthini , R. Jeyabalan ^*
Department of Mathematics, Alagappa University, Karaikudi, Tamilnadu, India

ABSTRACT

A vertex N-magic total labeling is a bijective function that maps the vertices and edges of a graph G onto the successive integers from 1 to p + q. The labeling exhibits two distinct properties: First, the count of unique magic constants k_i for i belonging to the set {1, 2, ...,N} is equivalent to the cardinality of N; secondly, the magic constants ki must be arranged in a strictly ascending order. In the present context, the constant N is employed to represent different degrees of vertices. The term “magic constant values k_i” for i ∈ {1, 2, ...,N} refers to specific numbers that exhibit unique and interesting properties and are employed in the context of this investigation. By adding up the weights of each vertex in V (G), we might receive a magical constant number k_i for i ∈ {1, 2, ...,N}. Within the scope of this study, we discuss the sharp bounds of vertex N-magic total labeling graphs. In terms of magic constants k_i for i ∈ {1, 2, ...,N}, we also found the requirement for vertex N-magic total labeling of trees. We investigated the potential for vertex N-magic total labeling at vertices in graphs with varying vertex degrees.

KEYWORDS
Vertex N - magic Total, Sharp Bounds, Sun Graph

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] R. Nishanthini , R. Jeyabalan , "Sharp Bounds on Vertex N-magic Total Labeling Graphs," Mathematics and Statistics, Vol. 12, No. 3, pp. 234 - 239, 2024. DOI: 10.13189/ms.2024.120303.

(b). APA Format:
R. Nishanthini , R. Jeyabalan (2024). Sharp Bounds on Vertex N-magic Total Labeling Graphs. Mathematics and Statistics, 12(3), 234 - 239. DOI: 10.13189/ms.2024.120303.