Degree-Magic Labelings on the Join and Composition of Complete Tripartite Graphs

Authors

  • Phaisatcha Inpoonjai Faculty of Sciences and Agricultural Technology, Rajamangala University of Technology Lanna Chiang Rai, Chiang Rai

DOI:

https://doi.org/10.26713/cma.v10i3.1157

Keywords:

Tripartite graph, Supermagic graph, Degree-magic graph, Balanced degree-magic graph

Abstract

A graph is called supermagic if there is a labeling of edges, where all edges are differently labeled with consecutive positive integers such that the sum of the labels of all edges, which are incident to each vertex of this graph, is a constant. 
A graph \(G\) is called degree-magic if all edges can be labeled by integers \(1,2,\ldots ,|E(G)|\) so that the sum of the labels of the edges which are incident to any vertex \(v\) is equal to \((1+|E(G)|)\deg(v)/2\). Degree-magic graphs extend supermagic regular graphs. In this paper, the necessary and sufficient conditions for the existence of degree-magic labelings of graphs obtained by taking the join and composition of complete tripartite graphs are found.

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References

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Published

30-09-2019
CITATION

How to Cite

Inpoonjai, P. (2019). Degree-Magic Labelings on the Join and Composition of Complete Tripartite Graphs. Communications in Mathematics and Applications, 10(3), 391–402. https://doi.org/10.26713/cma.v10i3.1157

Issue

Vol. 10 No. 3 (2019)

Section

Research Article

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