Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 8 2 2025 02 20 On the Index Set of Complete Multipartite Graphs 227 232 466 10.22128/ansne.2025.941.1125 EN Samaneh Bahramian Semnan Branch, Islamic Azad University, Semnan, Iran 0000-0002-1710-0126 Journal Article 2025 01 14 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 $i=1,\ldots,t$). index set magic null set zero-sum https://ansne.du.ac.ir/article_466_65d920abe2faa047e9811f01ce35e865.pdf