On the Index Set of Complete Multipartite Graphs

Document Type : Research Article

Author

Semnan Branch, Islamic Azad University, Semnan, Iran

Abstract

For an undirected graph G‎, ‎and an abelian group A‎, ‎an A-magic labelling is an assignment of non-zero element of A‎, ‎to the edges of G‎, ‎such that the sum of the values of all edges incident with each vertex is constant‎. ‎A constant on magic sum is called an index set of G‎. ‎Shiu and Low proved that‎, ‎zero is in the index set of complete multipartite graph‎. ‎In this paper‎, ‎for $t\geq2$ we determine the index set of the complete multipartite graph $K_{n_{1},\ldots,n_{t}}$‎, ‎where $n_{i}\geq2$ (for $i=1,\ldots,t$).

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References

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Analytical and Numerical Solutions for Nonlinear Equations
Volume 8, Issue 2
December 2023
Pages 227-232

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History

  • Receive Date: 14 January 2025
  • Revise Date: 12 February 2025
  • Accept Date: 17 February 2025
  • Publish Date: 20 February 2025

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