Publication: On Even Vertex Magic Total Labelings of Plus Wheels and Some Wheel-Related Graphs
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Issued Date
2026-02-01
Resource Type
eISSN
22277390
Scopus ID
2-s2.0-105031454191
Journal Title
Mathematics
Volume
14
Issue
4
Rights Holder(s)
SCOPUS
Bibliographic Citation
Mathematics Vol.14 No.4 (2026)
Suggested Citation
Saduakdee S., Khemmani V. On Even Vertex Magic Total Labelings of Plus Wheels and Some Wheel-Related Graphs. Mathematics Vol.14 No.4 (2026). doi:10.3390/math14040583 Retrieved from: https://hdl.handle.net/20.500.14740/55358
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Abstract
Let G be a graph with n vertices and m edges. A vertex magic total labeling of G is a bijection (Formula presented.) such that, for each vertex (Formula presented.), the sum of the label of u and the labels of all edges incident to u is equal to a fixed constant, referred to as the magic constant. A vertex magic total labeling is said to be even if the labels assigned to the vertices are exactly even numbers (Formula presented.). These labelings, along with related variations, have theoretical significance and practical applications, such as resource allocation, fault tolerance, and network design. Structured labelings aid channel assignment, address computation, and reduce collisions in networks. In this paper, we investigate wheel-related graphs that either admit or do not admit an even vertex magic total labeling. Furthermore, we introduce a new class of wheel-related graph, referred to as the plus wheel (Formula presented.), that can have such labelings, and we also establish a necessary and sufficient condition for such graphs to possess this property.