### Journals Information

**
Mathematics and Statistics Vol. 12(3), pp. 234 - 239 DOI: 10.13189/ms.2024.120303 Reprint (PDF) (245Kb) **

## 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.